Three-dimensional nanoscale metrology using FIRAT probe

ABSTRACT

In accordance with an embodiment of the invention, there is a force sensor for a probe based instrument. The force sensor can comprise a detection surface and a flexible mechanical structure disposed a first distance above the detection surface so as to form a gap between the flexible mechanical structure and the detection surface, wherein the flexible mechanical structure is configured to deflect upon exposure to an external force, thereby changing the first distance over a selected portion of the gap, the change in distance at the selected portion orienting a probe tip of the force sensor for multi-directional measurement.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 60/730,217, filed Oct. 25, 2005, the entirety ofwhich is hereby incorporated herein by reference.

This application is divisional of, and claims the benefit of U.S. patentapplication Ser. No. 12/136,399, filed Jun. 10, 2008, which is acontinuation of, and claims the benefit of, U.S. patent application Ser.No. 11/552,274, filed Oct. 24, 2006, which issued as U.S. Pat. No.7,395,698 on Jul. 8, 2008, the entirety of each of which is herebyincorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The subject matter of this application relates to probe microscopy. Moreparticularly, the subject matter of this application relates to methodsand devices for probe and force microscopes with sensors having improvedsensitivity.

2. Description of the Prior Art

Conventional atomic force microscope (AFM) and its variations have beenused to probe a wide range of physical and biological processes,including mechanical properties of single molecules, electric andmagnetic fields of single atoms and electrons. Moreover, cantileverbased structures inspired by the AFM have been a significant driver fornanotechnology resulting in chemical sensor arrays, various forms oflithography tools with high resolution, and terabit level data storagesystems. Despite the current rate of success, the AFM needs to beimproved in terms of speed, sensitivity, and an ability to generatequantitative data on the chemical and mechanical properties of thesample. For example, when measuring molecular dynamics at roomtemperature, the molecular forces need to be measured in a time scalethat is less than the time of the thermal fluctuations to break thebonds. This requires a high speed system with sub-nanoNewton andsub-nanometer sensitivity.

Current cantilever-based structures for AFM probes and their respectiveactuation methodologies lack speed and sensitivity and have hinderedprogress in the aforementioned areas. Imaging systems based on smallcantilevers have been developed to increase the speed of AFMs, but thisapproach has not yet found wide use due to demanding constraints onoptical detection and bulky actuators. Several methods have beendeveloped for quantitative elasticity measurements, but the trade-offbetween force resolution, measurement speed, and cantilever stiffnesshas been problematic especially for samples with high compliance andhigh adhesion. Cantilever deflection signals measured during tappingmode imaging have been inverted to obtain elasticity information withsmaller impact forces, but complicated dynamic response of thecantilever increases the noise level and prevents calculation of theinteraction forces. Arrays of AFM cantilevers with integratedpiezoelectric actuators have been developed for parallel lithography,but complex fabrication methods have limited their use.

Most of the scanning probe microscopy techniques, including tapping modeimaging and force spectroscopy, rely on measurement of the deflection ofa microcantilever with a sharp tip. Therefore, the resulting force datadepend on the dynamic properties of the cantilever, which shapes thefrequency response. This can be quite limiting, as mechanical structureslike cantilevers are resonant vibrating structures and they provideinformation mostly only around these resonances. For example, in tappingmode imaging it is nearly impossible to recover all the informationabout the tip-sample interaction force, since the transient forceapplied at each tap cannot be observed as a clean time signal.

Moreover, conventional methods of imaging with scanning probes can betime consuming while others are often destructive because they requirestatic tip-sample contact. Dynamic operation of AFM, such as thetapping-mode, greatly reduces shear forces during the scan. However, theonly free variable in this mode, the phase, is related to the energydissipation and it is difficult to interpret. Further, the inverseproblem of gathering the time-domain interaction forces from the tappingsignal is not easily solvable due to complex dynamics of the AFMcantilever. Harmonic imaging is useful to analyze the sample elasticproperties, but this method recovers only a small part of the tip-sampleinteraction force frequency spectrum.

Thus, there is a need to overcome these and other problems of the priorart associated with probe microscopy.

SUMMARY OF THE INVENTION

In accordance with an embodiment of the invention, there is a forcesensor for a probe based instrument. The force sensor can comprise adetection surface and a flexible mechanical structure disposed a firstdistance above the detection surface so as to form a gap between theflexible mechanical structure and the detection surface, wherein theflexible mechanical structure is configured to deflect upon exposure toan external force, thereby changing the first distance.

According to another embodiment of the invention, there is a forcesensor structure. The force sensor structure can comprise a cantileverand a force sensor positioned on a free end of the cantilever. The forcesensor can comprise a gap formed by a detection surface at the free endof the cantilever and at least one sidewall for positioning a flexiblemechanical structure a first distance from the detection surface.

According to another embodiment of the invention, there is a forcesensor unit. The force sensor unit can comprise a force sensor and adetector. The force sensor can comprise a detection surface and aflexible mechanical structure positioned a distance above the detectionsurface to form a gap, the flexible mechanical structure configured todeflect upon exposure to an external stimuli. The detector can beconfigured to detect deflection of the flexible mechanical structure.

According to another embodiment of the invention, there is another forcesensor. The force sensor can comprise a substrate comprising an opticalport having an optical axis, a reflective diffraction grating positionedalong the optical axis and positioned a distance from the optical port,and a cantilever positioned a distance from the substrate. Thecantilever can comprise a fixed end in contact with the substrate, afree end positioned a distance from the diffraction grating, wherein aportion of the free end is positioned along the optical axis, and aprobe tip in contact with the free end of the cantilever.

It can be understood that both the foregoing general description and thefollowing detailed description are exemplary and explanatory only andare not restrictive of the invention, as claimed.

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate several embodiments of theinvention and together with the description, serve to explain theprinciples of the invention.

BRIEF DESCRIPTION OF THE FIGURES OF THE DRAWINGS

FIG. 1A shows a cross-sectional schematic diagram of an exemplary forcesensor in accordance with the present teachings.

FIG. 1B shows a scanning electron microscope (SEM) picture of anexemplary force sensor in accordance with the present teachings.

FIG. 1C shows a photograph of a top down view of a force sensor inaccordance with the present teachings.

FIG. 1D shows a photograph of a bottom up view of a force sensor inaccordance with the present teachings.

FIG. 1E shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 2A shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 2B shows a scanning ion beam image of another exemplary forcesensor in accordance with the present teachings.

FIG. 2C shows photograph of a bottom up view of a force sensor inaccordance with the present teachings.

FIG. 2D shows a scanning electron microscope (SEM) picture of a forcesensor tip in accordance with the present teachings.

FIG. 3A shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 3B shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 4A shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 4B shows a bottom up view perspective of another exemplary forcesensor in accordance with the present teachings.

FIG. 4C shows a cross-sectional schematic diagram of an exemplary forcesensor in accordance with the present teachings.

FIG. 5A shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 5B is a graph plotting cantilever motion versus time for anexemplary force sensor in accordance with the present teachings.

FIG. 5C is a graph plotting flexible mechanical structuregrating-distance versus time for an exemplary force sensor in accordancewith the present teachings.

FIG. 6 shows a partial cross-sectional schematic diagram of anotherexemplary force sensor in accordance with the present teachings.

FIG. 7 shows a partial cross-sectional schematic diagram of anotherexemplary force sensor in accordance with the present teachings.

FIG. 8A shows a cross-sectional schematic diagram of an arrangement usedto monitor sensitivity of an exemplary force sensor in accordance withthe present teachings.

FIG. 8B shows a graph plotting voltage output versus time for a tappingcantilever for a force sensor in accordance with the present teachings.

FIG. 8C shows a close up of a portion of the graph shown in FIG. 8B.

FIG. 9A shows a schematic diagram of another exemplary force sensor inaccordance with the present teachings.

FIG. 9B shows a graph of interaction force versus time for an exemplaryforce sensor in accordance with the present teachings.

FIGS. 9C-9F show graphs of a flexible mechanical structure displacementversus time for an exemplary force sensor in accordance with the presentteachings.

FIGS. 9G-9H show graphs of photo-detector output versus time for anexemplary force sensor in accordance with the present teachings.

FIG. 10A shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 10B shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 10C shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 10D shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 11A shows a schematic diagram of another exemplary force sensor inaccordance with the present teachings.

FIG. 11B shows a schematic diagram of another exemplary force sensor inaccordance with the present teachings.

FIG. 11C shows a schematic diagram of another exemplary force sensor inaccordance with the present teachings.

FIG. 12 shows a schematic diagram of another exemplary force sensor inaccordance with the present teachings.

FIG. 13A shows a schematic diagram of another exemplary force sensor inaccordance with the present teachings.

FIG. 13B shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 14 shows a schematic diagram of an exemplary AFM system inaccordance with the present teachings.

FIGS. 15A-15C show graphs of interaction force versus time for anexemplary force sensor in accordance with the present teachings.

FIG. 16A shows a graph of interaction force versus time for an exemplaryforce sensor in accordance with the present teachings.

FIG. 16B shows a PAF image and a topography image of a sample using anexemplary force sensor in accordance with the present teachings.

FIG. 16C shows a PRF image and a topography image of a sample using anexemplary force sensor in accordance with the present teachings.

FIG. 17A shows a topographical image of a sample using an exemplaryforce sensor in accordance with the present teachings.

FIG. 17B shows line scans of the sample shown in FIG. 17A measured atdifferent speeds.

FIG. 17C shows a topographical image of sample in FIG. 17A made using aconventional AFM system.

FIG. 17D shows line scans of the sample shown in FIG. 17C measured atdifferent speeds using a conventional AFM system.

FIG. 18 shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 19 shows a graph plotting normalized intensity versus gap thicknessusing a force sensor in accordance with the present teachings.

FIG. 20A shows a graph plotting photo-detector output versus biasvoltage for a force sensor in accordance with the present teachings.

FIG. 20B shows a graph plotting photo-detector output versus time for aforce sensor in accordance with the present teachings.

FIG. 21 shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 22 shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 23A shows a graph plotting normalized intensity versus gapthickness using a force sensor in accordance with the present teachings.

FIG. 23B shows a graph plotting sensitivity versus metal thickness usinga force sensor in accordance with the present teachings.

FIG. 24A shows a graph plotting detector output versus bias voltageusing a force sensor in accordance with the present teachings.

FIG. 24B shows a graph plotting detector output versus bias voltageusing a force sensor in accordance with the present teachings.

FIG. 24C shows a graph plotting photo-detector output versus time usinga force sensor in accordance with the present teachings.

FIG. 25 shows a graph plotting normalized intensity versus gap thicknessusing a force sensor in accordance with the present teachings.

FIG. 26 shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 27 shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 28A shows a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings.

FIG. 28B shows a cross-sectional schematic diagram of a portion of theforce sensor shown in FIG. 28A in accordance with the present teachings.

FIG. 29A shows a top schematic diagram of an exemplary force sensorstructure with multiple integrated actuators accordance with the presentteachings.

FIG. 29B shows a cross-sectional schematic diagram of a portion of theforce sensor structure shown in FIG. 29A in accordance with the presentteachings.

FIG. 30 shows a cross-sectional schematic diagram of an oscillation ofthe force sensor in accordance with the present teachings.

FIG. 31A shows a side schematic diagram of a force sensor oscillation inaccordance with the present teachings.

FIG. 31B shows a side schematic diagram of a further force sensoroscillation in accordance with the present teachings.

FIG. 32 shows a side schematic diagram of a linear oscillation of theforce sensor in accordance with the present teachings.

FIG. 33 shows a side schematic diagram of a lateral oscillation of theforce sensor in accordance with the present teachings.

FIG. 34A shows a side schematic diagram of a force sensor havingmultiple optical detection ports in accordance with the presentteachings.

FIG. 34B shows a top schematic diagram of the force sensor shown in FIG.34A showing the location of gratings with different periods inaccordance with the present teachings.

FIG. 34C shows a top schematic diagram of the force sensor shown in FIG.34A showing the location of gratings with different orientations inaccordance with the present teachings.

FIG. 35 shows a side schematic diagram of a force sensor having athree-dimensional force measurement capability in accordance with thepresent teachings.

FIG. 36A shows a signal process for obtaining lateral tapping signalswith the force sensor in accordance with the present teachings.

FIG. 36B shows a signal process for obtaining vertical tapping signalswith the force sensor in accordance with the present teachings.

FIG. 37 shows a signal processing for non-contact three-dimensionalimaging with the exemplary force sensor in accordance with the presentteachings.

DETAILED DESCRIPTION OF THE INVENTION

In the following description, reference is made to the accompanyingdrawings that form a part thereof, and in which is shown by way ofillustration specific exemplary embodiments in which the invention maybe practiced. These embodiments are described in sufficient detail toenable those skilled in the art to practice the invention and it is tobe understood that other embodiments may be utilized and that changesmay be made without departing from the scope of the invention. Thefollowing description is, therefore, not to be taken in a limited sense.

Notwithstanding that the numerical ranges and parameters setting forththe broad scope of the invention are approximations, the numericalvalues set forth in the specific examples are reported as precisely aspossible. Any numerical value, however, inherently contains certainerrors necessarily resulting from the standard deviation found in theirrespective testing measurements. Moreover, all ranges disclosed hereinare to be understood to encompass any and all sub-ranges subsumedtherein. For example, a range of “less than 10” can include any and allsub-ranges between (and including) the minimum value of zero and themaximum value of 10, that is, any and all sub-ranges having a minimumvalue of equal to or greater than zero and a maximum value of equal toor less than 10, e.g., 1 to 5.

According to various embodiments there is a force sensor for use in, forexample, probe based instruments, such as probe microscopy and structuremanipulation. The force sensor can comprise a detection surface, aflexible mechanical structure, and a gap between the detection surfaceand the flexible mechanical structure. The force sensors can alsocomprise a tip in contact with the flexible mechanical structure.

Force sensors described herein can eliminate the corruption of utility,such as measurement information, that can arise from a cantilever. Theseforce sensors can also be used as actuators to apply known forces,providing clean and valuable elasticity information data on surfaces,biomolecules, and other materials. Moreover, these force sensors can beintegrated on cantilevers and can be compatible with existing AFMsystems while providing accurate tip displacement and also act as“active tips”.

According to various embodiments, a displacement measurement can be madeusing a flexible mechanical structure, such as a membrane, a diaphragm,a cantilever, a clamped-clamped beam, a flexible structure comprisingmultiple flexible elements partially or totally fixed at one end on asubstantially rigid surface and connected at a point so as to form asymmetry axis. These flexible mechanical structures can bemicro-machined. These flexible mechanical structures can have uniform ornon-uniform cross sections to achieve desired static and dynamicdeflection characteristics. For example, the vibration modes that aresymmetric and anti-symmetric with respect to the symmetry axis can beused to detect forces in different directions. These flexible mechanicalstructures can be made of metals such as gold, aluminum, or asemiconductor such as single crystal silicon or polycrystalline silicon,or dielectric materials such as silicon nitride, silicon oxide, or apolymer such as SU-8, or they can be a composite structure of metallic,semiconducting, polymer, or dielectric materials. While not intending tobe so limited, measurements can be made to detect, for example:localized forces, such as, a force experienced by a tip contacting theflexible mechanical structure; surface topography using for example, aflexible mechanical structure with an integrated tip contacting asurface; a flexible mechanical structure with an integrated tip in closeproximity of a surface or substance; and forces between a reactivesubstance, such as a molecule, bound to the flexible mechanicalstructure and another reactive substance, such as a molecule, bound on aclose by structure such as a tip.

According to various embodiments, the detection surface can be a surfaceof a rigid substrate, or a part of a rigid substrate, with an opticallyreflective diffraction grating, a part of a rigid substrate with areflective and/or electrically conductive diffraction grating foroptical interferometric detection and electrostatic actuation, a part ofa rigid substrate with electrically conductive members for electrostaticactuation and capacitive detection, a surface of a rigid substrate witha semi-transparent layer for optical interferometry. In some cases thedetection surface can be a surface of a deformable mechanical structuresuch as a membrane, clamped-clamped beam or a cantilever. The rigidityof the mechanical structure with the detection surface can besubstantially higher than the flexible mechanical structure of the forcesensor. The detection surface can contain conductive and dielectricportions to have electrical isolation between actuation and detectionelectrodes. In some cases, the deformable detection surface can beactuated and therefore it can contain a separate electrode orpiezoelectric film for actuation purposes. Still further, in some casesthe detection surface can form a substrate.

According to various embodiments, displacement can be measured usinginterferometric techniques or capacitive techniques. For example, agrating, such as that used in a diffraction based opticalinterferometric method or any other optical interferometric method suchas, for example, Fabry-Perot structures, an example of which isdescribed in U.S. patent application Ser. No. 10/704,932, filed Nov. 10,2003, which is incorporated herein by reference in its entirety, can beused. Capacitive measurements can use techniques used to monitorcapacitance, such as that used in capacitive microphones.

The flexible mechanical structure dimensions and materials can beadjusted to have desired compliance and measurement capabilities to makestatic and dynamic measurements with sufficient bandwidth. The overallshape of the flexible mechanical structure can be circular, square, orany other suitable shape. Typical lateral dimensions can be from 1 μm to2 mm, flexible mechanical structure thickness can be from 10 nm to 3 μm,and the gap can be from 1 nm to 10 μm. In some embodiments the gap canbe as large as 1 mm. The flexible mechanical structure material cancomprise, for example, aluminum, gold, silicon nitride, silicon, siliconoxide, or polysilicon or can be a composite structure of metallic,semiconducting, and dielectric materials. The gap can be sealed orpartially sealed for applications in liquids, or it can be open forvacuum and atmospheric measurements.

For some force measurements, a soft cantilever may not be required.Using the output from the force sensors in a feedback loop, one can usean external actuator to individually adjust the tip-flexible mechanicalstructure, tip-sample distances. According to various embodiments, theflexible mechanical structure can be electrostatically actuated to applydesired forces. According to various embodiments, force sensorsdescribed herein can be attached to a cantilever to form a force sensorstructure. Further, the force sensor structure can be combined with adetector to form a force sensor unit that can be used in a probe basedinstrument.

FIG. 1A shows a cross-sectional schematic diagram of an exemplary forcesensor 100 in accordance with the present teachings. The force sensor100 comprises a detection surface 102 and a flexible mechanicalstructure 104. The flexible mechanical structure 104 can be disposeddistance (D) above the detection surface so as to form a gap 105 betweenthe flexible mechanical structure 104 and the detection surface 102. Theflexible mechanical structure can be configured to move to a newposition 104′ upon exposure to external stimuli 114, such as a force.Moreover, the force sensor 100 can include elements configured to detectchanges in the distance (D). Still further, the force sensor 100 can beactuated to affect the distance (D) using, for example, bottom electrode106, such as a grating, and a top electrode 116, both of which aredescribed in more detail below.

The detection surface 102 can be made of a material transparent topredetermined wavelengths of light. For example, the detection surfacecan be made from silicon oxide, such as quartz. The overall shape of theflexible mechanical structure 104 can be circular, square, or any othersuitable shape. Typical diameters of flexible mechanical structure 104can range from about 5 μm to about 2 mm and the thickness of flexiblemechanical structure 104 can be from about 10 nm to about 10 μm. Theflexible mechanical structure can be a micro-machined material that cancomprise, for example, aluminum, gold, silicon nitride, silicon oxide,or polysilicon.

According to various embodiments, the distance (D) of gap 105 can befrom about 50 nm to about 50 μm. Moreover, the gap 105 can be sealed forapplications in liquids, or it can be open for vacuum and atmosphericmeasurements. In some embodiments, the gap can be formed by the flexiblemechanical structure and can be supported over the detection surface byat least one sidewall. Movement of the flexible mechanical structure, ordisplacement measurements, can be made, for example using a grating asdescribed below, which uses a diffraction based optical interferometricmethod or any other optical interferometric method or a capacitivemethod, such as in that used in capacitive microphones, can be used fordetection. According to various embodiments, grating periods of thegrating 106 can range from about 0.5 m to about 20 m. The incident lightcan be from the UV (with wavelengths starting at about 0.2 m) to IR(with wavelengths starting at about 1.5 m).

FIGS. 1B-1D show various perspective views of exemplary force sensors.For example, FIG. 1B shows a view using a scanning electron microscope(SEM) of the sensor 100. FIG. 1C is a top down photographic view of theforce sensor 100 and shows flexible mechanical structure 104. FIG. 1D isa photographic view of the force sensor 100 as seen by passing lightthrough the transparent detection surface 102 and shows grating 106positioned under the flexible mechanical structure 104.

According to various embodiments, the force sensor 100 can also includea grating 106, as shown in FIG. 1E. In FIG. 1E, a beam of light 110 canbe directed through the detection surface 102 to impinge on the flexiblemechanical structure 104 and the grating 106. According to variousembodiments, the beam of light 110 can be directed at the detectionsurface 102 at an angle, such as, in the range of, for example ±10° awayfrom normal to the detection surface 102. A portion of the flexiblemechanical structure 104 can be reflective such that light 110 can bereflected from the flexible mechanical structure 104 and another portioncan be reflected by the grating 106. As a result, different diffractionorders with different intensity levels can be generated as the lightpasses through the grating 106 depending on the gap thickness.

For example, FIG. 1E shows first diffraction order light 112 reflectedfrom the grating 106 and the flexible mechanical structure 104. Thediffracted light 112 can be detected by a detector 108. It is to beunderstood that alternatively, the detectors can be used to detectchanges in capacitence due to changes in the gap 105.

As shown in FIG. 1E, a stimuli 114, such as a force, can be applied tothe flexible mechanical structure 104. The stimuli 114 causes theflexible mechanical structure 104 to bend, or flex, shown as 104′.According to various embodiments, the flexible mechanical structure 104can bend in various directions, such as toward the detection surface 102or away from the detection surface 102. Bending the flexible mechanicalstructure 104 causes the thickness (D) of the gap 105 shown in FIG. 1Ato change.

When using a beam of light, the light 110 is reflected in a differentdirection when the flexible mechanical structure is in the bent position104′ than when the flexible mechanical structure is in the rest position104. Further, light 110 reflected from the bent flexible mechanicalstructure 104′ interacts differently with the grating 106 to producechanges in the intensity of different diffraction orders, shown in FIG.1E as 112 a-112 c. The detectors 108 can then detect the intensity ofthe diffracted light output from the grating 106. This provides arobust, micro-scale interferometer structure. Generally, informationobtained from the detectors 108 can be used to determine the stimuli114, such as the amount of force, applied to the flexible mechanicalstructure 104. This determination can be done using a computer processor(not shown) or other various techniques as will be known to one ofordinary skill in the art. Also shown in FIG. 1E is a top electrode 116that can cooperate with, for example grating 106, to serve as anactuator, as will be described in detail below.

According to various embodiments the detector 108 can be aphoto-detector, such as a silicon photodiode operated in photovoltaic orreverse biased mode or another type of photo-detector sensitive in thewavelength range of the light source. Moreover, the light 110 can be acoherent light source such as a laser. Exemplary light sources caninclude, but are not limited to, helium neon type gas lasers,semiconductor laser diodes, vertical cavity surface emitting lasers,light emitting diodes.

FIG. 2A shows a cross-sectional schematic diagram of another exemplaryforce sensor 200 in accordance with the present teachings. The forcesensor 200 comprises a detection surface 202, a flexible mechanicalstructure 204, a grating 206, and a tip 207. In some embodiments, theforce sensor 200 can also include a top electrode 216. Moreover, thegrating 206 can be covered with a dielectric layer to prevent electricalshorting in case of flexible mechanical structure collapse.

Generally, the force sensor 200 can be used to manipulate structures,such as atoms, molecules, or micro-electromechanical systems (MEMS) orto characterize various material properties of a sample 218. Forexample, the topography of the sample 218 can be determined by movingthe sample 218 in a lateral direction across the tip 207. It is alsocontemplated that the sample 218 can remain stationary and the tip 207can be moved relative to the sample 218. Changes in height of the sample218 are detected and cause the tip 207 to move accordingly. The force onthe tip 207 caused by, for example the tip motion, can cause theflexible mechanical structure 204 to bend, or flex as shown by 204′.Light 210 can also be directed through detection surface 202 to impingeon the flexible mechanical structure 204. The light 210 is reflectedfrom the flexible mechanical structure and diffracted by the grating206. As the tip 207 applies force to the flexible mechanical structure,the thickness of the gap 205 changes. This can cause the reflected lightto diffract differently than if the flexible mechanical structure werein its un-bent position. Thus, different diffraction orders of intensitycan change depending on the gap thickness.

After passing through the grating 206 the diffracted light 212 a-c canbe detected by the detectors 208. The output from the detectors 208 canbe used in a feedback loop to direct an external actuator (not shown) toadjust the tip-flexible mechanical structure position (i.e., the gapheight), and thus the tip-sample distance (d). The flexible mechanicalstructure 204 can be electrostatically actuated to apply desired forcesor to adjust the flexible mechanical structure position (i.e., the gapheight), and thus the tip-sample distance (d) by biasing electrodes 220a and 220 b attached to the grating 206 and the top electrode 216,respectively. Although two detectors are shown in FIG. 2A, one ofordinary skill in the art understands that one or more detectors can beused.

According to various embodiments, the force sensor 200 can form anintegrated phase-sensitive diffraction grating structure that canmeasure the flexible mechanical structure 204 and/or tip 207displacement with the sensitivity of a Michelson interferometer. Thedisplacement of the tip 207 due to stimuli acting on it can be monitoredby illuminating the diffraction grating 206 through the transparentdetection surface 202 with a coherent light source 210 and the intensityof the reflected diffraction orders 212 a-c can be recorded by thedetectors 208 at fixed locations. The resulting interference curve istypically periodic with λ/2, where λ is the optical wavelength in air.According to an exemplary embodiment, the displacement detection can bewithin the range of about λ/4 (167.5 nm for λ=670 nm) in the case of afixed grating 206. However, the detection surface 202 and the grating206 can be moved by suitable actuators to extend this imaging range.Furthermore, the grating 206 can be located not at the center but closerto the clamped edges of the flexible mechanical structure to increasethe equivalent detectable tip motion range. In the case of a microscope,the “active” tip can be moved by electrostatic forces applied to theflexible mechanical structure 204 using the diffraction grating 206 asan integrated rigid actuator electrode. In some applications, thisactuator can be used to adjust the tip 207 position for optimaldisplacement sensitivity to provide a force feedback signal to anexternal actuator moving the transparent detection surface 202.

In some embodiments, such as applications requiring high speeds, thisintegrated actuator can be used as the only actuator in the feedbackloop to move the tip 207 with a speed determined by the flexiblemechanical structure 204 dynamics in liquids, air, and vacuum.

FIG. 2B shows a focused ion beam (FIB) micrograph of a force sensor 250according to an exemplary embodiment. In the embodiment shown in FIG.2B, the flexible mechanical structure 254 is 0.9 μm thick and is madefrom aluminum. Moreover, the flexible mechanical structure 254 is 150 μmin diameter and it can be formed by sputter deposition on a 0.5 mm thickquartz substrate over a 1.4 μm thick photoresist sacrificial layer. FIG.2C shows the optical micrograph of the flexible mechanical structure 254from the backside as seen through the substrate 252. The grating 256 andthe electrical connections 270 can be seen as well as the darker spot atthe position of the tip 257 at the middle of the flexible mechanicalstructure 254. In FIG. 2C, the 90 nm thick aluminum grating 256 can beformed by evaporation over a 30 nm thick titanium or titanium nitrideadhesion layer and then patterned to have a 4 μm grating period with 50%fill factor. A 220 nm thick oxide layer can be deposited over thegrating 256 using plasma enhanced chemical vapor deposition. In thiscase, the subsequent flexible mechanical structure stiffness wasmeasured to be approximately 133 N/m using a calibrated AFM cantileverand the electrostatic actuation range was approximately 470 nm beforecollapse. The tip 257 was fabricated out of platinum using an FIB. Theprocess involved ion beam assisted chemical vapor deposition of platinumusing methyl platinum gas where molecules adsorb on the surface but onlydecompose where the ion beam interacts. The tip 257, with a radius ofcurvatures down to 50 nm on the aluminum flexible mechanical structures254, was fabricated with this method. An SEM micrograph of a typical tipwith 70 nm radius of curvature is shown in FIG. 2D.

According to various embodiments, the force sensor 200 can have acompact integrated electrostatic actuator, where the electric fieldbetween the grating electrode 206 and the top electrode 216 is containedwithin the gap 205. This structure can be replicated to form planararrays of sensors, as described in more detail below, with goodelectrical and mechanical isolation. With a suitable set of flexiblemechanical structure and electrode materials, the device can be operatedin a dielectric or conductive fluid. According to various embodiments,the electrostatic forces may act only on the probe flexible mechanicalstructure 204. As such, the actuation speed can be quite fast.Therefore, combined with array operations, the force sensor can be usedin probe applications that call for high speeds.

FIG. 3A depicts a schematic diagram of another exemplary force sensor300 and FIG. 3B depicts a schematic diagram of multiple force sensors300 working in concert in accordance with the present teachings. Theembodiments shown in FIGS. 3A and 3B can be used as force sensors forparallel force measurements, such as in the case of biomolecularmechanics. The force sensors 300 shown in FIGS. 3A and 3B can comprise adetection surface 302 and a flexible mechanical structure 304. The forcesensor 300 can also comprise a grating 306 and a tip 307 positionedabove the flexible mechanical structure 304. According to variousembodiments, reactive substances, such as molecules, includingbiomolecules, labeled 318 a and 318 b in FIGS. 3A and 3B can be attachedto flexible mechanical structure 304 and tip 307, respectively. In someembodiments, the force sensors 300 can also include a top electrode 316.FIG. 3B shows the force sensors 300 in contact with a single detectionsurface 302. However, in some cases more than one force sensor 300 cancontact a separate detection surface so as to be controlled separately.

The force sensors 300 can be used to characterize various materialproperties of the reactive substance. For example, biomolecular bondingcan be determined by moving the tip 307 contacted by a reactivesubstance, including, for example, inorganic molecules and/or organicmolecules, such as biomolecules, over the force sensors 300. It is alsocontemplated that the tip 307 can remain stationary and the forcesensors 300 can be moved relative to the tip 307. The reactive substanceon the flexible mechanical structure 304 can be attracted to thereactive substance on the tip 307. A stimuli 319, such as a force,light, or temperature, on, for example, the force sensor 300 or the tip307 caused by, for example the molecular attraction, a light source, ora temperature source, can cause the flexible mechanical structure 304 tobend, or flex as shown by 304′. Light 310 can also be directed throughdetection surface 302 to impinge on the flexible mechanical structure.The light 310 is reflected from the flexible mechanical structure andthen diffracted by the grating 306. As the stimuli displaces theflexible mechanical structure, the thickness of the gap 305 changes.This can cause the reflected light to diffract differently than if theflexible mechanical structure were in its un-bent position. Thus,different diffraction order intensities can be generated as the lightpasses through the grating 306 depending on the gap thickness. Afterpassing through the grating 306 the diffracted light 312 a-c can bedetected by the detectors 308. The output from the detectors 308 can beused in a feedback loop to direct an external actuator (not shown) toadjust the flexible mechanical structure position (i.e., the gapheight), and thus the tip-sample distance (d). According to variousembodiments, the flexible mechanical structure 304 can beelectrostatically actuated to apply desired forces by biasing electrodes320 a and 320 b attached to the grating 306 and the top electrode 316,respectively.

By using a variety of techniques disclosed herein, displacements from 1mm down to 1×10⁻⁶ Å/√Hz or lower can be measured. As such, forces from1N down to 1 pN can be detected with 10 kHz bandwidth with an effectivespring constant of the sensor flexible mechanical structure from about0.001N/m to about 1000N/m at its softest point. These mechanicalparameters can be achieved by micro-machined flexible mechanicalstructures, such as MEMs microphone flexible mechanical structures.Therefore, using flexible mechanical structure surfaces and tipsfunctionalized by interacting reactive substances, as shown in FIGS. 3Aand 3B, force spectroscopy measurements can be performed in parallelusing optical or electrostatic readout.

For example, in the case of rupture force measurements, the reactivesubstance, such as a molecule, is pulled and if the bond is intact, theflexible mechanical structure is also pulled out while the displacement,i.e., applied force, is measured. With the bond rupture, the flexiblemechanical structure comes back to rest position. The force sensorflexible mechanical structures can be individually actuated to applypulling forces to individual molecules and measuring their extensionsallowing for array operation.

FIGS. 4A-4C depict perspective views of exemplary embodiments inaccordance with the present teachings. FIG. 4A depicts a cross-sectionalschematic diagram and FIG. 4B depicts a view of the top of a forcesensor structure 400. The force sensor structure 400 can include acantilever 422, such as that used in AFM, and a force sensor 401positioned on the free end of the cantilever 422. The force sensor 401can comprise a detection surface 402, a flexible mechanical structure404, a gap 405, grating 406, a tip 407, and a top electrode 416.Further, the cantilever 422 can be transparent to allow for opticalreadout of the deflection of the flexible mechanical structure, whichhas an integrated tip for imaging. The cantilever 422 can be made ofmaterials similar to those of the detection surface material, describedabove. Indeed, in some embodiments, the cantilever 422 alone cancomprise the detection surface 402. Alternatively, the detection surfacecan be a substrate formed on the cantilever. In some embodiments thecantilever 422 can also include a reflector 424.

The cantilever 422 can be used to provide periodic tapping impact forcefor tapping mode imaging to apply controlled forces for contact mode ormolecular pulling experiments. Because the flexible mechanical structure404 can be stiffer than the cantilever 422 and can be damped byimmersion in a liquid, the measurement bandwidth can be much larger thanthe cantilever 422. Furthermore, optical readout of the diffractionorders can directly provide tip displacement because the diffractionorders can be generated by the grating 406 under the flexible mechanicalstructure 404.

According to various embodiments, the reflector 424 can be used to beambounce to find cantilever deflection for feedback, if needed. In somecases, the tip-force sensor output can provide the real force feedbacksignal. The cantilever 422 and the flexible mechanical structure 404dimensions can be adjusted for the measurement speed and forcerequirements.

FIG. 4C depicts a cross-sectional schematic diagram of another exemplaryforce sensor 401 a in accordance with the present teachings. The forcesensor 401 a is similar to the force sensor 401 but includes a thickerbase region 403 of the detection surface 402. Also shown in FIG. 4C areelectrical connections 420 a and 420 b that contact the grating 406 andthe top electrode 416, respectively. The electrical connections can beused to provide electrostatic actuation or capacitive detection.

FIG. 5A shows an embodiment of a force sensor structure 500 according tothe present teaching for tapping mode imaging. In addition totopography, tapping mode can also provide material property imaging andmeasurement if the tip-sample interaction forces can be accuratelymeasured. The disclosed force sensor structure solves a significantproblem for this mode of operation. For example, when the cantilever isvibrated using a sinusoidal drive signal, shown in FIG. 5B, and it isbrought to a certain distance to the surface, the tip starts to contactthe surface during a short period of each cycle, as shown in FIG. 5C.While the oscillation amplitude is kept constant for topographyinformation, the contact force i.e., the tip-sample interaction forceand duration can be related to the material properties of the sample andadhesion forces. With a regular cantilever, the deflection signal can bedominated by the vibration modes of the cantilever, which cansignificantly attenuate the information in the harmonics. According tovarious embodiments, the transient force that the tip 507 or the sample518 experiences at each tap can be measured. Because the force sensorsdisclosed herein can directly measure the flexible mechanicalstructure/tip displacement directly using optical interferometry orcapacitive measurement, this transient force signal can be obtained. Bydesigning the flexible mechanical structure stiffness, broadbandresponse is possible and short transient force signals can be measured.This situation can be valid in both air and liquids, as the informationis independent of the cantilever vibration spectrum.

Using electrically isolated electrodes, the flexible mechanicalstructure can be actuated so as to have an “active tip”. Further theactuated flexible mechanical structure can optimize the opticaldetection or capacitive detection sensitivity in air or in liquidenvironments. FIG. 6 shows an application of a force sensor structure600 comprising a sensor 601 on a cantilever 622 where the tip 607 isactive, as shown by arrow 623. In FIG. 6, the active tip 607 can be usedto apply known forces to the surface of sample 618 using electrostaticactuation and optical interferometric displacement detection orcapacitive displacement detection can be achieved. The tip 607 can beactivated, for example, by applying a bias between the grating 606 andthe top electrode 616. Further, a DC force, shown by arrow 626, can beused to keep the tip 607 in constant contact with the sample.

Light 610 can be directed to the flexible mechanical structure 604 andthe orders 612 a-c of light diffracted by the grating 606 can bedetected by the detector 608. Similar to the force sensor 401 a shown inFIG. 4C, designing the dimensions of the flexible mechanical structurebase 603, or choosing the operation frequency at an anti-resonance ofthe cantilever, the flexible mechanical structure 604 can be moved, andhence the tip 607 can be pushed into the sample 618 by knownelectrostatic forces. Accordingly, displacements of the flexiblemechanical structure 604 can be measured optically or capacitively.Furthermore, in some embodiments there is no need for an active tip onthe force sensor. Moreover for optical measurements, the gap between theflexible mechanical structure and the grating can be optimized duringfabrication of the force sensor. Thus, there is no need to activelyadjust that gap during tapping mode operation as shown in FIG. 6.Similarly for capacitive detection, an electrical connection fordetection of capacitance changes can be provided. In that case, theforce sensor 601 can be connected to a detection circuit such as used ina capacitive microphone for measuring the force on the tip 607.

The thickness of the base 603 (or the substrate) supporting the flexiblemechanical structure 604 can be adjusted to control the operationfrequency to insure that the motion of the flexible mechanical structure604 produces an indentation in the sample surface. This measurement,therefore, directly provides surface elasticity information. Accordingto various embodiments, the frequency of electrostatic actuation can bein the ultrasonic range. Alternatively, a wideband impulse force can beapplied and resulting displacements can be detected in the bandwidth ofthe flexible mechanical structure displacement force sensor. For theseapplications, it may be desirable to move the higher cantilevervibration mode frequencies away from the first resonance. This can beachieved, for example, by increasing the mass close to the tip of thecantilever, such as by adjusting the thickness, or mass of the base 603.With added mass, the cantilever acts more like a single mode mass springsystem and can generate tapping signals without spurious vibrations andcan also be effective at a broad range of frequencies.

In general, for tapping mode AFM and UAFM applications a broadband,stiff tip displacement measurement sensor/structure can be integratedinto compliant structures, such as regular AFM cantilevers. Althoughflexible mechanical structures are primarily described here, accordingto another embodiment, the tip displacement measurement structure can bea stiff beam structure with the same cross-section of the flexiblemechanical structure or another stiff cantilever, as shown, for example,in FIG. 7. In FIG. 7, there is a force sensor structure 700, comprisinga force sensor 701, a compliant structure 722, a tip 707, and a flexiblemechanical structure 728 such as a stiff broadband structure. In thiscase, the stiff broadband structure 728 can be small cantilever mountedto an end of the compliant structure 722, also a cantilever. The smallcantilever 728 can be spaced a distance (d) from the compliant structure722. The compliant structure 722 can be used to control the impactand/or contact force of the tip 707 mounted to a side of the stiffbroadband structure 728. Further, the stiff broadband structure 728 canbe used to measure tip displacements. Displacement of the tip 707 can bemeasured, for example, optically, electrostatically, capacitively,piezoelectrically or piezoresistively.

According to various embodiments, for fast imaging and tapping modeapplications, the cantilever can be eliminated. In this case, a fast x-yscan of a sample or the integrated tip can be used with the describedsensor/actuator for tapping and detecting forces. The large, fast z-axismotion can be generated, for example, by a piezoelectric actuator thatmoves the base of the force sensor, which can be a thick, rigidsubstrate.

The sensitivity of a force sensor in accordance with the presentteachings can be described by the following exemplary embodiment,depicted in FIG. 8A. In FIG. 8A, a rectangular silicon AFM cantilever822 with a tip 807 is vibrated at 57 kHz above a 150 μm diameter, ˜1 μmthick aluminum flexible mechanical structure 804 with an integrateddiffraction grating 806. The force sensor 800 flexible mechanicalstructure 804 is built on a quartz detection surface or substrate 802. ADC bias of 37V is applied to move the flexible mechanical structure 804to a position of optimal detection sensitivity and the vibrating tip 807is brought close enough to have tapping mode-like operation withintermittent contact. Diffraction order 812 can be detected by detector808 when a beam 810 is diffracted by grating 806 upon exiting forcesensor 800.

The single shot signals collected at this position are shown at the toptwo rows (Row 1 and Row 2) of the four rows of the graph in FIG. 8B. Thebottom graph, in FIG. 8C, shows a zoomed in version of Row 2 ofindividual taps, where the transient displacement of the flexiblemechanical structure due to impact of the tip is clearly seen. If theflexible mechanical structure material were softer or there were acompliant coating on the flexible mechanical structure 804, the measuredtap signals would be longer in duration and smaller in amplitude becausethe tip 807 would spend more time indenting the softer surface whiletransmitting less force to the flexible mechanical structure 804.Therefore, the tapping force measurement provides elasticity informationand this embodiment can be used as a material property sensor for a thinfilm coating on the flexible mechanical structure.

In addition, when the tip 807 leaves contact, the flexible mechanicalstructure 804 is pulled away due to adhesion or capillary forces,permitting force spectroscopy measurement methods. When the tip 807 ismoved progressively closer, it is in contact with the flexiblemechanical structure 804 for a longer duration of each cycle and finallyit pushes the flexible mechanical structure 804 down during the wholecycle. Thus, the simple force sensing structures disclosed hereinprovide information not available by conventional AFM methods and resultin more effective tools for force spectroscopy applications.

The sensitivity of another force sensor in accordance with the presentteaching can be described by the following exemplary embodiment,depicted in FIGS. 9A-9H. As shown in FIG. 9A, a quartz substrate 902with a sensor flexible mechanical structure 904 is placed on apiezoelectric stack transducer 927, which can be used to approach to thetip 907 and obtain force distance curves. The flexible mechanicalstructure 904 is aluminum and can be 150 μm in diameter, 1 μm thick, andlocated over a 2 μm gap 905 above the rigid diffraction gratingelectrode 906. In this case, the grating period is 4 μm. The gap 905 isopen to air through several sacrificial layer etch holes (not shown).The grating 906 can be illuminated at 910 through the quartz substrate902 using, for example, a HeNe laser (λ=632 nm) at a 5° angle away fromnormal to the substrate. The output optical signal can be obtained byrecording the intensity of the 1^(st) diffraction order beam 912 b.

For measuring the AFM dynamic tip-sample interaction forces, thecantilever 922 can be glued on a piezoelectric AC drive transducer 926that can drive the cantilever 922 at its resonant frequency. Theflexible mechanical structure 904, with a stiffness of approximately76N/m as measured at the center using a calibrated AFM cantilever 922,can be used. The DC bias on the flexible mechanical structure 904 isadjusted to 27V to optimize the optical detection, and the sensitivityis calibrated as 16 mV/nm by contacting the flexible mechanicalstructure 904 with a calibrated AFM cantilever 922 and a calibratedpiezo driver. In this case, the broadband RMS noise level of the systemwas about 3 mV (0.18 nm) without much effort to reduce mechanical,laser, or electrical noise.

A force curve can be produced by moving the piezoelectric stack 927supporting the substrate 902 with a 20 Hz, 850 nm triangular signal andmaking sure that there is tip-flexible mechanical structure contactduring a portion of the signal period. The cantilever 922 can be, forexample, a FESP from Veeco Metrology, Santa Barbara, Calif., withk=2.8N/m.

FIG. 9B shows a force curve 950 where the inset drawings (i)-(v)indicate the shape of the cantilever 922 and flexible mechanicalstructure 904, and the hollow arrow indicates the direction of motion ofthe piezo stack 927 and the quartz substrate 902. Moreover, the insertdrawings (i)-(v) correspond to sections (a)-(e), respectively, of thecurve 950. Before measurement, the flexible mechanical structure 904 isat rest, as seen in insert (i) and section (a). Tip-flexible mechanicalstructure contact happens starting in section (b) at around 3 ms and thetip bends the flexible mechanical structure 904 downwards, as shown ininsert drawings (ii) and (iii). Tip-flexible mechanical structurecontact continues through section (c) until about 26 ms, which is insection (d). The piezoelectric motion is reversed starting at section(c). Section (d) shows that attractive forces due to adhesion pulls theflexible mechanical structure 904 up, as seen in insert (iv), for 2 msand then the flexible mechanical structure 904 moves back to its restposition, as seen in insert (v) after a 180 nN jump at the end of theretract section. Curve 950 in section (e) shows the rest position.

For direct observation of time resolved dynamic interaction forces alongthe force curve, a similar experiment can be performed while thecantilever 922 is driven into oscillation by applying a sinusoidalsignal to the AC drive piezo 926 at 67.3 kHz. The single shot, transientflexible mechanical structure displacement signal 960 obtained during acycle of the 20 Hz drive signal is shown in FIG. 9C. Dynamic interactionforce measurements provide various types of information, as indicated bythe various interaction regimes (A)-(C) during the measurement. The dataof FIG. 9C is shown expanded in FIGS. 9D-F in the initial tapping region(A), intermittent to continuous contact region (B), and continuous tointermittent contact transition region (C), respectively.

Starting from the left, the cantilever tip 907 is first out of contactwith the flexible mechanical structure 904. At around 1 ms it startsintermittent contact (tapping) with the flexible mechanical structure904 as individual taps are detected, as shown in FIG. 9D. As thecantilever 922 gets closer to the flexible mechanical structure 904, thepulses become uni-polar and the distortion is more severe as there aredouble peaked tap signals when the cantilever 922 gets into contact dueto non-linear interaction forces, as shown FIG. 9E. When the tip 907 isin continuous contact, which happens around 4.2 ms, the displacementsignal has the periodicity of the drive signal in addition to distortionthat can be caused by contact non-linearities and higher order vibrationmodes of the cantilever 922 with its tip 907 hinged on the flexiblemechanical structure 904. Similarly, around 15 ms, the cantilever 922starts breaking off the flexible mechanical structure surface andtapping resumes, as shown in FIG. 9F. Between 7 ms and 12 ms the curveis not linear.

Individual tapping signals can be filtered by the dynamic response ofthe flexible mechanical structure 904. In this example, the force sensorwas not optimized and the flexible mechanical structure 904 acted as alightly damped resonator with a resonant frequency at 620 kHz ratherthan having broadband frequency response that is ideal for fastinteraction force measurements. Nevertheless, the transfer function ofthe flexible mechanical structure 904 can be obtained using, forexample, integrated electrostatic actuators, as described herein.

Still further, FIG. 9G shows the measured temporal response of theflexible mechanical structure 904 when a 2V square pulse 100 ns inlength is applied in addition to the 27V DC bias at the actuatorterminals. Comparing the trace waveform in FIG. 9G with averaged datafrom individual tap signals shown in FIG. 9H, it can be seen that thestiff cantilever tap is nearly an impulsive force, which can berecovered by inverse filtering.

Thus, according to various embodiments, minimum displacement detectionlevels down to 10⁻⁴ Å/√Hz can be measured and mechanical structures withspring constants in the 0.001 to 10N/m range can be built that canmonitor force levels in the pico-Newton range. These sensitivity levelscan make it useful for a wide range of probe microscopy applicationsincluding quantitative interaction force measurements, fast imaging inliquids and in air, and probe arrays for imaging, lithography, andsingle molecule force spectroscopy.

While FIGS. 8A-9H are examples of sensitivity testing made by applying aforce from a tip to the force sensor, similar sensitivities can beachieved when a tip is mounted to the force sensor and the force sensoris used to characterize a sample.

FIG. 10A depicts a cross-sectional schematic diagram of anotherexemplary force sensor 1000 in accordance with the present teachings.The sensor 1000 can comprise a substrate 1002, a flexible mechanicalstructure 1004, a gap 1005, a tip 1007, a plurality of separate topelectrodes, such as electrodes 1016 a-c, and a bottom electrode 1030.The force sensor 1000 substrate 1002 can be positioned at an end of acantilever 1022. According to various embodiments, the flexiblemechanical structure 1004 can be fully clamped around its circumferenceas described above and shown in FIG. 10A. Alternatively, the flexiblemechanical structure 1004 can be a clamped-clamped beam with arectangular or H-shape, as shown in FIGS. 10B and 10C, respectively,where the short edges 1040 at the ends are clamped. Still further, theflexible mechanical structure 1004 can be a cantilever structure or asimilar structure that changes shape in a predictable manner in responseto a force applied to the tip 1007, as shown in FIG. 10D.

Each of the plurality of separate top electrodes 1016 a-c can beelectrically isolated and formed in the flexible mechanical structure1004. Moreover, the bottom electrode 1030 can spaced apart from theseparate top electrodes 1016 a-c by the gap 1005. Further, the bottomelectrode can be positioned in the substrate 1002 and can be contactedby electrode terminals 1020 d. Similarly, each of the separate topelectrodes 1016 a-c can be contacted by electrode terminals 1020 a-c. Insome cases, the electrode terminals 1020 a-c and 1020 d can becapacitive sensing terminals that can detect a capacitance change formedbetween the separate top electrodes 1016 a-c and the bottom electrode1030.

In FIG. 10A, a voltage can be applied between the electrode terminals1020 a-c and 1020 d. The voltage can be used to independently controland move any of the separate top electrodes 1016 a-c, so that they canserve as actuators. Further, the separate top electrodes 1016 a-c canalso perform sensing, similar to that of a dual electrode capacitivemicromachined ultrasonic transducer where the vibrations of the sensorflexible mechanical structure are converted to electrical currentsignals through change in capacitance.

For example, the force sensor 1000 can be used for fast imaging wherebias voltages are applied between the electrode terminals 1020 a, 1020 cand the bottom electrode terminal 1020 d and alternating voltages of thesame or reverse phase are applied to the electrode terminals 1020 a and1020 c to vibrate the tip 1007 vertically or laterally to haveintermittent contact with a sample surface. In some cases, the forcesbetween the tip 1007 and a close by surface can be sensed withoutcontact for non-contact imaging. The bias voltages applied to theelectrode terminals 1020 a, 1020 c also control the position of the tip1007 in response to changes in capacitance detected between theelectrode terminals 1020 b and the bottom electrode terminal 1020 d. Anexternal controller (not shown) can read the detected capacitance changeand generate the control signals (bias voltages) applied to theelectrode terminals 1020 a, 1020 c and the bottom electrode terminal1020 d.

FIG. 11A depicts a cross-sectional schematic diagram of anotherexemplary force sensor unit 1100 in accordance with the presentteachings. The force sensor unit 1100 can comprise a force sensor 1101,a detection surface 1102, a flexible mechanical structure 1104, a gap1105, a tip 1107, a plurality of separate top electrodes, such aselectrodes 1116 a-c, a plurality of gratings, such as first grating 1106a and second grating 1106 b, at least one detector 1108, and acantilever 1122. The first grating 1106 a can have a different gratingspacing than the grating spacing of 1106 b. Furthermore, the firstgrating 1106 a can have a different orientation as compared to thegrating 1106 b. It is to be understood that other force sensorembodiments described herein can also comprise multiple gratings.

The detection surface 1102 can be positioned at a free end of thecantilever 1122. Moreover, the flexible mechanical structure 1104 can befully clamped around its circumference, it can be a clamped-clamped beamwith a rectangular or H shape where the short edges at the ends areclamped, or it can be a cantilever structure or a similar structure thatchanges shape in a predictable manner in response to a force applied tothe tip 1107.

The force sensor 1101 shown in FIG. 11A can be used for lateral force orfriction measurements. For example, force sensor 1101 can be used tosense torsion created on the flexible mechanical structure, shown as1104′. Separate top electrodes 1116 a-c can be positioned on theflexible mechanical structure 1104 to excite the torsional motion orresonances. Similarly, the flexible mechanical structure 1104 can bebent asymmetrically, shown as 1104′, due to torsion created by the tip1107 or due to out of phase actuation from the first grating 1106 a, thesecond grating 1106 b, and the top electrodes 1116 a-c acting aselectrostatic actuators. In particular, a voltage can be applied to theelectrical contacts 1120 a and 1120 b that contact the first grating1106 a and the top electrode 1116 a, respectively. The same voltage canbe applied to the electrical contacts 1120 c and 1120 d that contact thetop electrode 1116 c and the second grating 1106 b, respectively.Applying this same voltage can cause the flexible mechanical structure1104 to bend up and down. In contrast, similarly applying a differentialvoltage can cause torsion of the flexible mechanical structure 1104.

A light beam 1110 can be directed through the detection surface 1102 toimpinge on the flexible mechanical structure 1104. The beam 1110reflects off of the flexible mechanical structure 1104, a portion ofwhich can be reflective, and is diffracted differently by the firstgrating 1106 a and the second grating 1106 b. As shown in FIG. 11A, thefirst grating 1106 a can generate a first set of diffraction orders 1112a-d and the second grating 1106 b can generate a second set ofdiffraction orders 1113 a-d. The detectors 1108 can detect the differentdiffraction orders. The detector outputs can be added to obtain up anddown bending displacement detection. Similarly, the outputs can besubtracted to obtain torsional motion and force detection. Thisinformation can be obtained when the spring constant for the secondbending mode (torsion around the mid axis) of the flexible mechanicalstructure 1104, clamped-clamped beam or a cantilever is known. Thus, inaddition to acting as actuators, the first grating 1106 a and secondgrating 1106 b can be used to optically or capacitively decouple thebending motion from the torsional motion. As such, the sensed outputs ofthese detectors yield both bending and torsional motion information. Onecan also use separate beams 1110 to illuminate the plurality ofgratings.

FIG. 11B depicts a cross-sectional schematic diagram of anotherexemplary force sensor unit 1150 in accordance with the presentteachings. The force sensor unit 1150 can comprise a force sensor 1151,a first detection surface 1152 such as a substrate, a flexiblemechanical structure 1154, a gap 1155, a tip 1157, a top electrode 1166,a grating 1156, grating flexible mechanical structure actuation inputs1170 a and 1170 b, and tip flexible mechanical structure actuationinputs 1172 a and 1172 b. The force sensor 1151 can be affixed to a freeend of a cantilever (not shown). The grating flexible mechanicalstructure actuation input 1170 a can contact a transparent conductor1173, such as indium tin oxide, formed on the first detection surface1152. According to various embodiments, the flexible mechanicalstructure 1154 can be separated from the grating by a distance (d).Moreover, the flexible mechanical structure 1154 can comprise the topelectrode 1166 and the grating 1156 can be spaced away from the firstdetection surface 1152.

The force sensor 1151 shown in FIG. 11B can extend the tip actuationrange without degradation in optical displacement measurementsensitivity. For example, the tip 1157 can be positioned at a relativelylarge distance away from the grating 1156. In this manner, the tip 1157can be moved large distances without shorting or damaging the sensor1150. Moreover, the grating 1156 can be actuated to keep the detectionsensitivity at an optimal level. For example, the grating can beactuated a distance of λ/4, where λ is the wavelength of light 1161, toprovide proper sensitivity.

The tip 1157 and flexible mechanical structure 1154 can be spaced awayfrom the grating in various ways. For example, rigid supports 1179 canbe formed on the first detection surface 1152 to support the flexiblemechanical structure 1154. In this manner, the flexible mechanicalstructure 1154 is separated from the grating 1156 at a predetermineddistance. A second detection surface 1184 can be separated from thefirst detection surface 1152 by a gap so as to provide a predeterminedseparation distance. The grating 1156 can be formed on the seconddetection surface 1184.

Operation of the sensor 1150 is similar to that described above. Forexample, light 1161 is directed through the first detection surface1152, which can be transparent. The light 1161 passes through thetransparent conductor 1173 and through the grating 1156 and impinges theflexible mechanical structure 1154. The light is reflected from theflexible mechanical structure 1154 and is diffracted by grating 1156before being detected by detectors 1158.

FIG. 11C depicts a cross-sectional schematic diagram of anotherexemplary force sensor 1190 in accordance with the present teachings.The force sensor 1190 can comprise a detection surface 1192, apiezoelectric actuator 1193 comprising a thin piezoelectric film 1193 adisposed between a pair of electrodes 1193 b and 1193 c, a flexiblemechanical structure 1194, a gap 1195, a tip 1197, and a grating 1196.The force sensor 1190 can be combined with at least one detector and acantilever to form a force sensor unit.

According to various embodiments, the thin piezoelectric film cancomprise a piezoelectric material such as, for example, ZnO or AlN. Thepiezoelectric film can be deposited and patterned on the flexiblemechanical structure 1194 along with the tip 1197. The piezoelectricactuator 1193 can form, for example, a bimorph structure that can bebent and vibrated by applying DC and AC signals through the electrodes1193 b and 1193 c. According to various embodiments, the grating 1196can be placed off-center so as to provide a large range of tip motionthat can be detected without losing sensitivity.

FIG. 12 depicts a cross-sectional schematic diagram of an array 1200 offorce sensors 1201 a-c in accordance with the present teachings. Thearray 1200 can comprise multiple force sensors, such as force sensors1201 a-c, formed on a detection surface 1202. Each of the force sensors1201 a-c can comprise a flexible mechanical structure 1204, a gap 1205,a tip 1207, an electrode, such as electrodes 1216 a-c, and a grating1206. According to various embodiments, the array 1200 of force sensorscan be used for imaging and sensing at the same time so as to enablesimultaneous sensing of a physical, chemical, or biological activity andimaging of the sample 1218 surface. The force sensors 1201 a-c can becombined with at least one detector 1208 and a cantilever (not shown) toform a force sensor unit. Some of the force sensors 1201 a-c can bemodified to include, for example, electrodes, sensitive films, oroptical waveguides, while the others can be used for regular probemicroscopy imaging of topography. Thus, each force sensor can performthe same or different function.

For example, force sensor 1201 a can be used to measure and image theelasticity or adhesion of the surface of sample 1218. Further, thegrating 1206 can be used with electrode 1216 a to provide actuation ofthe flexible mechanical structure 1204 by applying a voltage betweencontacts 1220 a and 1220 b, respectively. The elasticity information canbe measured by applying known dynamic and quasi-static forces to thesurface with the tip 1207 using an external actuator or by applyingvoltage to the terminals 1220 a and 1220 b. At the same time, thediffraction order intensities can be monitored by the optical detectors1208 or a capacitance change can be detected by electrical means todetermine the resulting tip displacement. Viscoelasticity or adhesioncan be calculated using computer models well known by those who areskilled in the art of probe microscopy.

Force sensor 1201 b can be used to measure and image the topography ofthe surface of sample 1218 similarly as described herein using beam 1210to generate diffraction orders 1212 a-c that can be detected bydetectors 1208. In the case of force sensor 1201 b, the grating 1206 canbe used with electrode 1216 b to provide actuation of the flexiblemechanical structure 1204 by applying a voltage between contacts 1220 cand 1220 d, respectively.

Still further, the force sensor 1201 c can be used to measure and imagethe surface potential of sample 1218. In the case of force sensor 1201c, the grating 1206 can be used with electrode 1216 c to provideactuation of the flexible mechanical structure 1204 by applying avoltage between contacts 1220 e and 1220 f, respectively. Moreover, thesample 1218 can be biased with respect to the tip 1207 of the forcesensor 1201 c using the electrical terminal 1220 g to assist in surfacepotential measurements. The tip 1207 on the force sensor 1216 c can havea separate electrical terminal 1220 h which is electrically isolatedfrom the other electrodes 1220 f and 1220 e and placed in the dielectricsensor flexible mechanical structure 1204. The surface potential canthen be measured using an electric potential measurement deviceconnected between terminals 1220 g and 1220 h. Furthermore, an externalsource (not shown) can be connected to terminals 1220 g and 1220 h andthe current flow in that electrical circuit can be measured to locallydetermine the flow of ions or electrons available from the sample 1218or in a solution that the force sensor 1216 c is immersed.

As described previously, the force sensors 1216 a and 1216 b can be usedto obtain surface topography and elasticity information. Thisinformation can be used by an external controller to adjust the positionof the tips 1207 of individual force sensors to optimize themeasurements. As such, the array 1200 can be used to measure elasticity,electrochemical potential, optical reflectivity, and fluorescence whilealso imaging the surface.

FIGS. 13A and 13B depict top-down and cross-sectional schematic diagramsof an exemplary force sensor 1300 in accordance with the presentteachings. In FIGS. 13A and 13B, the force sensor 1300 can comprise adetection surface 1302, a grating 1306, a tip 1307, an electrostaticcantilever actuator flexible mechanical structure 1317, and a cantilever1322. As shown in FIG. 13B, the force sensor 1300 can also include anoptical port that can be created, for example, by etching a hole 1332through the detection surface 1302. According to various embodiments,the grating 1306 can be a diffraction grating comprising a plurality ofconductive fingers that can be deformable and that can beelectrostatically actuated independently of the cantilever 1322 in orderto control the relative gap 1305 distance (d) between the grating 1306and the reflecting cantilever 1322. Further, the cantilever 1322 canhave its own electrostatic actuation mechanism 1317. With the cantilever1322 having its own electrostatic actuation mechanism 1317, displacementmeasurements can be optimized on each cantilever 1322 of an array ofindependent force sensor structures. With this capability, the initialpositions from topography, misalignment with the imaged sample, and/orprocess non-uniformities can be measured and corrected.

In operation, as shown, for example, in FIG. 13B, a light 1310 can bedirected at the cantilever 1322 through the hole 1332. The light 1310 isreflected from the cantilever and then diffracted by the grating 1306.Various diffraction orders 1312 a-c can be detected by detectors 1308.

FIG. 14 shows a force sensor structure 1400 used in an AFM system 1401according to various embodiments. The AFM system 1401 can comprise aforce sensor 1403, a detector 1408, such as a photodiode, a light source1411, such as a laser diode, and a computer 1430 comprising a firstprocessor 1440 to generate a control loop for imaging materialproperties and a second processor 1450 to generate a control loop forfast tapping mode imaging. The second processor 1450 can further controlan integrated electrostatic actuator, as described herein.

As shown in FIG. 14, the force sensor 1403 can be fabricated, forexample, on a detection surface 1402 and placed on a holder 1428, whichcan be attached to an external piezoelectric actuator (piezo tube) 1427.The intensity of, for example, the +1^(st) diffraction order of lightdiffracted by a grating 1406 in the force sensor 1403 is detected by thedetector 1408 as the tip 1407 displacement signal. For example, with a 4μm grating period and a 670 nm laser wavelength, the +1^(st) diffractionorder is reflected at a 9.6° angle from the grating normal. Tilting thedetection surface 1402 by 6.2° with respect to the incident beam 1410provides a total of 22° angular deflection. According to variousembodiments with the force sensor 1403, significantly all of the light1410 can be reflected from the grating 1406 and the flexible mechanicalstructure 1404, eliminating optical interference problems due toreflections from the sample 1418. This can provide a clean backgroundfor tip displacement measurements.

The performance of the AFM 1401 having a force sensor, such as thosedescribed herein, can be characterized using an integrated electrostaticactuator. For example, an optical interference curve with a DC biasrange of 24-36 V was traced and the bias was adjusted for optimumsensitivity point at 30 V. The displacement sensitivity at this biaslevel was 204 mV/nm. The RMS noise measured in the full DC-800 kHzbandwidth of the photodetector 1408 was 18 mV RMS. This value, confirmedby spectrum analyzer measurements, corresponds to 1×10⁻³ Å/√Hz minimumdetectable displacement noise with 1/f corner frequency of 100 Hz. Usingthe laser power available from the 0^(th) and −1^(st) orders anddifferential detection, this value can be lowered well below 5×10⁻⁴Å/√Hz without increasing the laser power or using etalon detection. Thedynamic response of a typical flexible mechanical structure was alsomeasured using electrostatic actuation, indicating a resonance frequencyof 720 kHz with a quality factor of 4.1, suitable for fast tapping modeimaging.

Two controller schemes interfaced with the AFM system 1401 can be used.The first scheme is used with the first processor 1440 comprising acontroller 1443 and an RMS detector 1445 for material propertymeasurement and imaging using transient interaction force signals. TheZ-input of the piezo tube 1427 is driven to generate a 2 kHz 120 nm peaksinusoidal signal while the controller 1443 keeps constant the RMS valueof the photo-detector signal generated by the force sensor 1403 when ittaps on the sample 1418. The 2 kHz signal frequency is chosen as acompromise between the ability to generate adequate vertical (Zdirection) displacement of the piezo tube and the frequency response ofthe internal RMS detector 1445 for a typical force sensor structure1401. The second controller scheme is used with the second processor1450 for fast tapping mode imaging. In this case, the Z-input of thepiezo tube is disabled and the integrated electrostatic actuator is usedto generate a 10 nm peak-to-peak free air tapping signal in the 500-700kHz range as well as the signals to control the force sensor 1403 tip1407 position keeping the RMS value of the tip vibration at the desiredset point.

FIGS. 15A-15C show the results of a force sensor described herein usedin a dynamic mode in an AFM system, such as that shown in FIG. 14. Theresults shown in FIGS. 15A-15C provide information about the transientinteraction forces with a resolution that exceeds conventional systems.In this example, the detection surface, such as a substrate, can beoscillated, and can be driven by a suitable actuator. Both theattractive and repulsive regions of the force curve are traced as thetip 1407 contacts the sample 1418 during some phases (I-V) of eachcycle. The inserts (i)-(v) in FIG. 15A show the shape of the flexiblemechanical structure 1404 during different phases of a cycle while thesubstrate is oscillated at 2 kHz by the Z-piezo. FIG. 15A also shows themeasured detector output signal during each phase corresponding to eachcycle. The detector 1408 output is proportional to the force acting onthe tip 1407.

In this particular case, during phase I, the tip 1407 is away from thesample 1418 surface where it experiences long range attractive forces.When brought close to the surface, the tip 1407 jumps to contact (0.2 nmchange in tip position, phase II) and remains in contact for about 14%of the cycle. In the middle of the period, the repulsive force appliedto the sample 1418 reaches to a peak value of 163 nN (1.22 nm tipdisplacement, phase III). When the tip 1407 is withdrawn, the tip 1407experiences capillary forces of 133 nN (phase IV) before breaking offfrom the liquid film on the sample 1418 surface (phase V). As shown inFIG. 15B, the controller 1443 of FIG. 14 can be used to stabilize thesignal with a constant RMS, so that the output signal of the forcesensor shows individual and repeatable taps on the sample 1418. Thesignals shown are averaged 100 times on a digitizing oscilloscope, andthe noise level is less than 1 nN with 800 kHz measurement bandwidth.

An application of this mode of operation is the measurement of localviscoelastic properties. For example, in FIG. 15C individual tap signalsobtained on (100) silicon (E=117 GPa) and photoresist (PR, Shipley 1813)(E=4 GPa) samples using a sensor with having a tip 50 nm radius ofcurvature were compared. The maximum repulsive force is significantlylarger for the silicon sample even though the tip-sample contact time isless than that of photoresist (PR) indicating that the silicon isstiffer than PR. Consequently, the positive slope of the time signalduring the initial contact to silicon sample is significantly largerthan it is when in contact with the PR sample. The silicon sample alsoshows higher capillary hysteresis. Both of these results are consistentwith existing models and data. Moreover, the tip 1407 can encounterdifferent long range van der Waals or electrostatic forces on these twosamples. Since this information is obtained with nanometer scale lateralresolution and applying nanoNewton level forces, this mode of operationcan be referred to as “nano-characterizer” mode of operation.

The results shown in FIGS. 15A-15C demonstrate a unique feature of theforce sensors described herein for dynamic force measurements. Inparticular, the output signal is generated only when there is aninteraction force on the tip. With broad bandwidth and high sensitivity,the force sensors enable direct measurement of transient interactionforces during each individual tap with high resolution and withoutbackground signal. This provides information on properties of the samplesuch as adhesion, capillary forces, as well as viscoelasticity.

The force sensor can be used to image various material properties byrecording at each pixel the salient features of the tap signal. Forexample, the AFM system 1401 shown in FIG. 14 can be used to monitortransient interaction forces. The first controller 1440 of system 1401can be used to maintain a constant RMS value of the output signal whilescanning the tapping tip 1407. FIG. 16A shows the transient tap signalson the PR and silicon regions of a sample having 360 nm thick, 2 μm widePR strips with 4 μm periodicity patterned on silicon surface.Significant differences exist between the tap signals in terms of boththe attractive and repulsive forces acting on the tip 1407. For example,the silicon surface exhibits a much larger adhesion force when comparedto the PR surface. Because the first controller 1440 attempts tomaintain a constant RMS value over the sample, it forces the tip 1407 toindent more into the PR region. As such, the tip 1407 experiences alarger repulsive force. The shape of the individual tap signals in theattractive region has a strong dependence on the environment.

To form an image in which sample adhesion dominates the contrastmechanism, a peak detector circuit can be used to record the peakattractive force (PAF) as the pixel value, such as points A_(si), A_(PR)in FIG. 16A. Simultaneously, the sample topography can be recorded usinga fixed RMS value set point. FIG. 16B shows the resulting adhesion (PAF)and topography images, 1661 and 1662, respectively, of the sample. Inthe topography image 1662, the stripes 1664 correspond to the 360 nmhigh PR pattern (Shipley 1805) and stripes 1665 correspond to thesilicon surface. In the PAF image 1661, the silicon surface appearsbrighter than PR due to higher adhesion forces. By recording the peakrepulsive force (PRF) as the pixel value, images where sampleviscoelasticity dominates the contrast, such as at points R_(si), R_(PR)in FIG. 16A, can be obtained.

Simultaneously recorded PRF and topography images of the same sampleregion are shown in FIG. 16C at 1671 and 1672, respectively. The PRFimage 1671 shows a reversed contrast when compared to the PAF image,while the topography image is repeatable. The PR strips 1674 appearbrighter in the PRF image as indicated by the individual tap signalsshown in FIG. 16A. Also, many more contamination particles are adheredto the silicon 1675 surface as compared to the PR strips 1674, and theseparticles are seen with high contrast. This is consistent with higheradhesion measured on the silicon in the PAF image 1661.

Although a simple controller based on the RMS value set point isdescribed in this embodiment, it is contemplated that different controlschemes, such as those sampling individual tap signals at desired timeinstants and using those values in the control loop can also be used.For example, if the peak value of the repulsive force is kept constantas the control variable, images where the contact-to-peak force timedetermines the contrast—a direct measure of sample stiffness can beobtained. Several existing models can then be used to convert theseimages to quantitative material properties. Similarly, by detecting theattractive force peaks before and after the contact one can obtainquantitative information on the hysteresis of the adhesion forces.

FIGS. 17A and 17B show the results of fast tapping mode imaging ofsample topography with a single sensor probe using the setup shown inFIG. 14. In this mode, the Z-input of the piezo tube 1427 isdisconnected and used only for x-y scan. The integrated electrostaticactuator is used for both oscillating the tip 1407 at 600 kHz andcontrolling the flexible mechanical structure 1404 bias level in orderto keep the oscillation amplitude constant as the tapping mode imagesare formed.

A standard calibration grating with 20 nm high, 1 μm wide, sharp stepswith 2 μm periodicity was used as the fast imaging sample (NGR-22010from Veeco Metrology). FIG. 17A shows the images of a 4 μm×250 nm area(512×16 pixels) of the grating with line scan rates of 1 Hz, 5 Hz, 20Hz, and 60 Hz. FIG. 17B shows the cross sectional profiles of individualscan lines for each image. The AFM system 1401 had an x-y scancapability that can go up to 60 Hz.

For comparison, FIGS. 17C and 17D, show the tapping mode images and linescans using a conventional AFM system on the same sample used in theexample of FIGS. 17A and 17B. The commercial AFM system used a tappingmode cantilever. The cantilever was made of silicon and had a 300 kHzresonance frequency (TESP-A from Veeco Metrology). In this case, thetapping piezo on the cantilever holder was used as the actuator.

As can be seen in the figures, AFM systems described herein are able toresolve the grating with at least a 20 Hz line scan rate and in somecases a 60 Hz line scan rate. In contrast, conventional AFM systems arenot able to follow the sharp steps starting at 5 Hz, and fail to producea viable image after 20 Hz line scan rate. The imaging bandwidth of theAFM system 1401 described herein was about 6 kHz. However, controllingthe dynamics of the air flow in and out of etch holes on two sides ofthe flexible mechanical structure, such as those shown at 280 in FIG.2C. With a sealed cavity, the imaging bandwidth of various force sensorsdescribed herein can be increased to more than 60 kHz. Moreover, sincethe force sensor unit is a well damped system even in air, methods otherthan RMS detection can be used to implement faster controllers.

FIG. 18 depicts a cross-sectional schematic diagram of another exemplaryforce sensor unit 1800 in accordance with the present teachings. FIG. 18shows a light source 1811 and a photodiode 1808 on the surface of anopaque, rigid, detection surface 1802. The detection surface 1802 can bea printed circuit board, a silicon wafer, or any other solid material.Furthermore, the light source 1811 and photodiode 1808 can beconstructed or sourced externally and attached to the detection surfaceor fabricated directly into the material using integrated circuit ormicromachining fabrication techniques.

The light source 1811 can be an optical fiber or the end of amicrofabricated waveguide with an appropriate reflector to direct thelight to the desired location in the force sensor unit 1800, such as adiffraction grating 1806. The optical diffraction grating structure 1806exists above the light source 1811, and is characterized by alternatingregions of reflective and transparent passages. A gap 1805 defining acavity is formed between the grating 1806 and the detection surface andcan be sealed at some desired pressure (including low pressures) withany gas or gas mixture, or can be open to ambient. Further, a flexiblemechanical structure 1804 (also called a reflective surface orreflective diaphragm) exists above the diffraction grating 1806 thatreflects light back towards the detection surface 1802. The diffractiongrating 1806 and the reflective surface 1804 together form a phasesensitive diffraction grating.

When illuminated with the light source 1811 as shown, diffracted lightreflects back towards the detection surface 1802 in the form ofdiffracted orders 1812 a and 1812 b with intensity depending on therelative position between the reflective surface 1804 and thediffraction grating 1806, or the gap 1805 thickness. The diffractedorders 1812 a and 1812 b emerge on both the right and left side and aretraditionally numbered as shown in FIG. 18. For the phase sensitivediffraction grating with 50% fill factor, i.e. reflective andtransparent passages with the same width, only the zero order and allodd orders emerge. The intensity of any one or any subset of theseorders can be measured with photo-diodes 1808 to obtain informationabout the relative distance between the diffraction grating 1806 and thereflective surface 1804. The angles of the orders are determined by thediffraction grating period, Λ_(g), and the wavelength of the incidentlight, λ. For example, in the far field the angle of the order n, θ_(n),will be given by the relation [1]:

$\begin{matrix}{{\sin\left( \theta_{n\;} \right)} = {n\;{\frac{\lambda}{\Lambda_{g\;}}.}}} & \lbrack 1\rbrack\end{matrix}$

In order to illustrate how the intensity of the reflected orders dependson the gap thickness, the normalized intensity of the zero and firstorders are plotted versus the gap in FIG. 19 assuming normal incidence.The remaining odd orders (i.e. 3^(th), 5^(th), etc.) are in phase withthe 1^(st) but have decreasing peak intensities. This behavior can beobtained when the light source 1811 remains coherent over the distancebetween the reflector and the diffraction grating 1806.

Furthermore, the diffracted orders can be steered to desired locationsusing structures such as Fresnel lenses. For this purpose, the gratings1806 can be curved or each grating finger can be divided into sectionsof sub-wavelength sized gratings.

Also using wavelength division multiplexing, light with differentwavelengths can be combined and used to illuminate a multiplicity offorce sensors with different grating periods. The reflected diffractionorders from different force sensors can either be converted toelectrical signals by separate photodetectors, or the reflected light atdifferent wavelengths can be combined in an optical waveguide or opticalfiber to minimize the number of optical connections to a processor thatsubsequently decodes the information carried at different wavelengths.Therefore, a multiplicity of force sensors can be interrogated using asingle physical link or a reduced number of physical links to aprocessing system.

According to various embodiments, such as chemical and biologicalsensors, the reflective surface 1804 can be made of single material or amulti layered material that changes its optical properties, such asreflectivity, in response to a chemical or biological agent. Similarly,the reflective surface 1804 can be a micromachined cantilever or abridge structure made of single or layered material that deforms due tothermal, chemical, magnetic, or other physical stimulus. For example, aninfrared (IR) sensor can be constructed by having a bimorph structureincluding an IR absorbing outer layer and a reflective layer facing thelight source 1811. In other embodiments, such as a microphone or apressure sensor, the reflector 1804 can be in the shape of a diaphragm.

In many applications, moving or controlling the position of thereflective surface 1804 may be desired for self-calibration, sensitivityoptimization, and signal modulation purposes. For example, if thereflective surface 1804 is a diaphragm or flexible mechanical structure,as in the case of a microphone or a capacitive micromachined transducer,vibrating the diaphragm to produce sound in a surrounding fluid may bedesired for transmission and self-calibration. Also, while measuring thedisplacement of the diaphragm, controlling the nominal gap 1805 heightto a position that will result in maximum possible sensitivity for themeasurement may be desired. These positions correspond to points ofmaximum slope on the curves in FIG. 19, where it can be seen graphicallythat a change in gap thickness results in a maximum change in intensityof the diffracted order. These examples can use an added actuationfunction that can be accomplished with electrostatic actuation. In oneexemplary embodiment, the entire diaphragm structure 1804 or just acertain region thereof can be made electrically conductive. This can beaccomplished by using a non-conductive material for the reflectivesurface 1804 such as a stretched polymer flexible mechanical structure,polysilicon, silicon-nitride, or silicon-carbide, and then making thematerial conductive in the desired regions either through doping or bydepositing and patterning a conductive material such as aluminum,silver, or any metal or doping the flexible mechanical structure 1804,such as when the flexible mechanical structure comprises polysilicon.

In another exemplary embodiment, the entire diffraction grating 1806 ora portion of the grating 1806 can be made conductive. The flexiblemechanical structure 1804 and diffraction grating 1806 can together forma capacitor which can hold charge under an applied voltage. The strengthof the attraction pressure generated by the charges can be adjusted bycontrolling the voltage, and precise control of the flexible mechanicalstructure 1804 position is possible.

FIGS. 20A and 20B demonstrate this function. First, increasing voltagelevels were applied to pull the flexible mechanical structure 1804towards the detection surface 1802, which resulted in decreasing gap1805 height (i.e. a movement from right to left on the curve in FIG.19). The change in light intensity of the first diffracted order thatresulted was measured with a photodiode and plotted at the top. Toillustrate why controlling the flexible mechanical structure positionmay be important, a displacement measurement of the flexible mechanicalstructure 1804 was made at different gap 1805 heights as follows. Atdifferent applied voltages, sound was used to vibrate the flexiblemechanical structure 1804 with constant displacement amplitude and theresulting change in light intensity of the first diffracted order wasagain measured with a photodetector. As shown in the bottom of FIG. 20A,voltage levels that move the gap height to a point corresponding to asteep slope of the optical curve are desirable as they produce largermeasurement signals for the same measured input. Although sound pressurewas used to displace the flexible mechanical structure 1804, the devicecan be tailored to measure any physical occurrence, such as a change intemperature or the exposure to a certain chemical, or an applied forceso long as the flexible mechanical structure 1804 was designed todisplace as a result of the occurrence.

This displacement measuring scheme has the sensitivity of a Michelsoninterferometer, which can be used to measure displacements down to1.4×10⁻⁵ Å for 1 Hz bandwidth for 1 mW laser power. Various embodimentsdisclosed herein can provide this interferometric sensitivity in a verysmall volume and can enable integration of light source, referencemirrors and detectors in a mechanically stable monolithic or hybridpackage. This compact implementation further reduces the mechanicalnoise in the system and also enables easy fabrication of arrays. Thehigh sensitivity and low noise achieved by the various embodiments farexceed the performance of other microphones or pressure sensors based oncapacitive detection.

FIG. 21 depicts a cross-sectional schematic diagram of another exemplaryforce sensor 2100 in accordance with the present teachings. FIG. 21shows a force sensor comprising a detection surface 2102, which allowsthe light source 2111 to be placed at a location behind the substrate2102. The detection surface 2102 also allows the reflected diffractedorders 2112 to pass through, and the light intensity of any of theseorders can measured at a location behind the substrate 2102. The forcesensor 2100 can also comprise a flexible mechanical structure 2104, suchas a diaphragm, and a diffraction grating 2106 that can be made moveableso that its position may be controlled via electrostatic actuation, witha region of the substrate serving as a bottom electrode 2116. Changingthe flexible mechanical structure—grating gap thickness can be used tooptimize the displacement sensitivity of the flexible mechanicalstructure, as discussed above with reference to FIG. 18.

Several material choices exist for the detection surface 2102 that istransparent at the wavelength of the incident light. These includequartz, sapphire, and many different types of glass, and it can besilicon for light in the certain region of the IR spectrum. Furthermore,several manufactures sell these materials as standard 100 mm diameter,500 μm thick wafers, which make them suitable for all micro-fabricationprocesses including lithographic patterning. As in the force sensor1800, several different material types may be used for the flexiblemechanical structure 2104, and the cavity between the platform anddiaphragm may be evacuated or filled with any type of gas mixture.

The diffraction grating 2106 may be made of any reflective material, aslong as the dimensions are chosen to produce a compliant structure thatmay be moved electrostatically. As explained for force sensor 1800,electrostatic actuation requires a top and bottom electrode. Accordingto various embodiments, the diffraction gating 2106 can serve as the topelectrode and the bottom electrode 2116 can be formed on the substrate2102. Furthermore, the distance between these electrodes can be small(order of a micrometer) to be able to perform the actuation withreasonable voltage levels (<100V). For example, for force sensor 2100this means regions of both the diffraction grating 2106 and thedetection surface 2102 can be made electrically conductive. If a metalor any other opaque material is chosen to form the bottom electrode 2116on the detection surface 2102, the electrode region should exist in aregion that will not interfere with the propagation of light towards thediffraction grating 2106 and the flexible mechanical structure 2104.Alternatively, a material that is both optically transparent andelectrically conductive, such as indium-tin oxide, may be used to formthe bottom electrode 2116 on the platform. Force sensor 2100 enables oneto use the advantages of electrostatic actuation while having a largedegree of freedom in designing the flexible mechanical structure 2104 interms of geometry and materials.

FIG. 22 depicts a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings. FIG. 22 shows theimplementation of a resonant-cavity-enhanced (Fabry-Perot cavity)optical force sensor 2200 that can be used to improve displacementsensitivity, which may be defined as the intensity variation of thediffracted beam per unit flexible mechanical structure displacement(i.e., the change of the cavity gap) due to the external excitation. Theforce sensor 2200 can comprise a detection surface 2202, two parallelmirror layers, such as a bottom mirror 2203 and a top mirror 2204, and agrating 2206. According to various embodiments, the bottom mirror 2203can be formed on the detection surface 2202 and can include the grating2206. Further, the top mirror 2204 can also serve as a diaphragm orflexible mechanical structure.

The bottom mirror 2203 and the top mirror 2204 can be separated by thegrating-embedded gap or cavity 2205, as illustrated in FIG. 22. Asmentioned, the flexible mechanical structure 2204 can have a highreflectance and can act as the top mirror, and the bottom mirror 2203can be placed beneath the diffraction grating 2206. The mirror layerscan be built, for example, using a thin metal film, a dielectric stackof alternating quarter-wave (λ/4) thick media, or combination of thesetwo materials.

FIG. 23A shows the calculated intensity of the first order versus thegap 2205 for the case of a metal mirror made of silver, but any othermetal with a high reflectivity and low loss at the desired wavelengthcan be used. It can be noticed that the change in the diffracted orderintensity with cavity gap 2205 in the resonant-cavity-enhanced opticalforce sensor 2200 departs from that shown in FIG. 19, depending onoptical properties of the mirror layers, such as reflectance. As seen inFIG. 23A, the slope of the intensity curve increases with increasingmetal layer thickness, hence the mirror reflectivity. The sensitivity inthe unit of photocurrent per flexible mechanical structure displacement(A/m) is also evaluated when the intensity of the first-order,diffracted from an incident light of 1 mW optical power, is detected bya detector, such as a photo-diode with 0.4 A/W responsivity. Thecalculation result for various metals is presented in FIG. 23B. Forexample, the displacement sensitivity can be improved by 15 dB using a20 nm thick silver layer for the mirror. For different metals withhigher optical loss, the improvement may be less or the sensitivity maydecrease as in the case of aluminum.

FIG. 24A shows the experimental data obtained by two structures with andwithout an approximately 15 nm thick silver mirror layer with analuminum diaphragm. FIG. 24A shows data for an embodiment without amirror. Similar to FIG. 20A, increasing the DC bias voltage helps one totrace the intensity curve in FIG. 24A from right to left. Because thereis no Fabry-Perot cavity formed in this embodiment, the intensity curveis smooth.

FIG. 24B shows the same curve for the Fabry-Perot cavity with a silvermirror. In this embodiment, the intensity curve has sharper features andlarge slopes around 16-18V DC bias. This is similar to the changepredicted in FIG. 23A. The sensitivity dependence is also verified bysubjecting the diaphragm to an external sound source at 20 kHz andrecording the first order intensity at different DC bias levels. FIG.24C shows the result of such an experiment and verifies that the opticaldetection signal is much larger for the 16V DC bias as compared to 40V,where the average intensity is the same. For a regular microphonewithout the Fabry-Perot cavity structure, one would expect to obtainlarger signal levels with 40V DC bias.

FIG. 25 shows the calculated intensity of the first order versus the gap2205 for the case of the dielectric mirrors. In this embodiment thedielectric mirrors are made of silver and SiO₂/Si₃N₄ pairs but any otherdielectric material combination resulting in a high reflectivity and lowloss at the desired wavelength can be used. The reflectance of themirror can be controlled by the change in the thickness of the metalfilm and the number of alternating dielectric pairs for a given choiceof mirror materials. In FIG. 25, the number of pairs is increased from 2to 8 and which in turn increases the slope of the intensity curveresulting in a higher sensitivity.

In contrast to the dielectric mirror case, peak intensity amplitude ofthe first order decreases with the metal mirror reflectance due to theoptical loss in the metal film (FIG. 23A), and thus metals of lowabsorption loss provide good results for the metal-mirror applications.In addition, the optimal bias position moves toward to a multiple of λ/2with the reflectance of the metal mirror. However, the optimal biasposition can be easily achieved through electrostatic actuation of theflexible mechanical structure 2204.

The scheme of the resonant-cavity-enhanced optical force sensor can bealso applied to the other microstructures described herein with a simplemodification of fabrication process.

FIG. 26 depicts a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings. FIG. 26 shows aforce sensor 2600 comprising a detection surface 2602, a flexiblemechanical structure 2604 (also called a diaphragm), a gap 2605 (alsocalled a cavity), and a grating 2606. The grating 2606 can be reflectiveand can be formed on the flexible mechanical structure 2604, which canbe transparent. Further, the grating can comprise reflective diffractionfingers. According to various embodiments, the detection surface 2602can be reflective. The force sensor 2600 can form a phase-sensitivediffraction grating when illuminated from the topside of the flexiblemechanical structure 2604 as shown in FIG. 26. Similar to the embodimentshown in FIG. 18, the zero and all odd orders of light are reflectedback and have intensities that depend on the gap 2605 between thediffraction grating 2606 and the detection surface 2602. The thicknessof the gap 2605 can also include the thickness of the flexiblemechanical structure 2604, which may be made of any transparentmaterial. Examples of transparent materials include silicon dioxide,silicon nitride, quartz, sapphire, or a stretched polymer membrane suchas parylene. Because the detection surface 2602 is reflective, anymaterial, including semiconductor substrates or plastics, can sufficegiven that they are coated with a reflective layer, such as metal. Toadd electrostatic actuation, as described herein, a region of both thedetection surface 2602 and the flexible mechanical structure 2604 can bemade electrically conductive. For the flexible mechanical structure2604, this can be accomplished by using a material that is bothreflective and electrically conductive for the diffraction grating 2606.For example, any reflective metal would be suitable. In variousembodiments, because the light source 2611 and detectors (not shown)exist on the top side of the flexible mechanical structure 2604, thisparticular embodiment offers remote sensing capabilities. For example,if measuring the displacement of the flexible mechanical structure 2604due to a change in pressure is desired (as would be the case for apressure sensor or a microphone), the detection surface 2602 can beattached to a surface and the light source 2611 and detectors can bestationed in a remote location, not necessarily close to the diaphragm.

In addition to remote measurements, the force sensor 2600 can beremotely actuated to modulate the output signal. For example, anacoustic signal at a desired frequency can be directed to the flexiblemechanical structure 2604 with the grating 2606 and the output signalcan be measured at the same frequency using a method such as a lock-inamplifier. The magnitude and phase of the output signal can giveinformation on the location of the flexible mechanical structure 2604 onthe optical intensity curve in shown in FIG. 19, which in turn maydepend on static pressure, and other parameters such as temperature,etc. Similar modulation techniques can be implemented usingelectromagnetic radiation, where an electrostatically biased flexiblemechanical structure with fixed charges on it can be moved by applyingelectromagnetic forces. In this case, the flexible mechanical structurecan be made of some dielectric material with low charge leakage.

FIG. 27 depicts a cross-sectional schematic diagram of another exemplaryforce sensor in accordance with the present teachings. FIG. 27 shows aforce sensor 2700 comprising a detection surface 2702, a transparentsupport comprising electrodes 2703, a flexible mechanical structure 2704(also called a diaphragm), a gap 2705 (also called a cavity), a grating2706, and a detector 2708. The detection surface 2702 in force sensor2700 can be transparent so that the light source 2711 and detectors 2708can be placed at a location behind the detection surface. However,placing the light source and detectors 2708 on the surface of thedetection surface is equally viable and allows the usage of substratessuch as silicon wafers or printed circuit boards. According to variousembodiments, the grating 2706 can be moveable. As discussed herein,controlling the gap 2705 between the grating 2706 and the reflectiveflexible mechanical structure 2704 can be used to optimize detectionsensitivity.

Various methods can be used to control the thickness of the gap 2705,such as, for example, controlling the flexible mechanical structure 2704position, the grating 2706 position, or both. Furthermore, the forcesensor 2700 allows placement of the grating 2706 anywhere in the cavity2705 between the light source 2711 and the flexible mechanical structure2704.

According to various embodiments, the use of highly reflectivesemi-transparent layers to enhance displacement sensitivity usingFabry-Perot cavity, as described by, for example the embodiment shown inFIG. 22. For example, a Fabry-Perot cavity can be implemented with anyof the other embodiments mentioned so far, when the semitransparentlayer is placed in close proximity to the diffraction grating.

For example, the sensors shown in FIGS. 18 and 21 can place asemi-transparent layer on the top or bottom surface of the grating.Further, the force sensor shown in FIG. 26 can place a semi-transparentlayer on either the top or backside of the flexible mechanicalstructure, which is where the diffraction grating is located in thiscase.

FIG. 28A depicts a cross-sectional schematic diagram of anotherexemplary force sensor in accordance with the present teachings. FIG.28A shows a force sensor 2800 comprising a detection surface 2802, aflexible mechanical structure 2804 (also called a diaphragm), a firstgap 2805A (also called a first cavity), a second gap 2805B (also calleda second cavity), a first grating 2806A (also called a referencegrating), a second grating 2806B (also called a sensing grating), adetector 2808, and a light source 2811. The second grating 2806B can beformed on the flexible mechanical structure 2804, which can betransparent. Moreover, the flexible mechanical structure 2804 can beformed over the first grating 2806A.

In this embodiment, the flexible mechanical structure 2804 is or has areflective diffraction grating, second grating 2806B, rather than amirror-like uniform reflector surface described above. Moreover, thesecond grating 2806B on the flexible mechanical structure 2804 reflectorcan have the same periodicity as the first grating 2806B, but can beoffset and can have diffraction fingers whose widths are smaller thanthe gap between the first grating 2806A. This offset allows some of theincident light to pass through. This structure, as shown in FIG. 28A,allows some of the incident light from light source 2811 to transmitthrough the whole force sensor 2800 and also introduces new diffractionorders in the reflected field. As such, this provides a different kindof phase grating than those described above.

FIG. 28B is provided to assist in understanding the operation of asensor having two gratings. For example, one can consider the phase ofthe light reflected from the first grating 2806A (also called thereference grating) (φ₁) and the second grating 2806B on the flexiblemechanical structure 2804 (φ₂). When the difference between φ₁ and φ₂ is2kπ, k=0, 2, 4, . . . , the apparent period of the grating is Λ_(g)(apparent reflectivity of 1, 0, 1, 0 regions assuming perfecttransmission through the transparent diaphragm 2804) and the evendiffraction orders are reflected with angles

$\begin{matrix}{{{\sin\left( \theta_{n} \right)} = {n\;\frac{\lambda}{\Lambda_{g}}}},{n = 0},{\pm 2},{{\pm 4}\mspace{14mu}\ldots}} & \lbrack 2\rbrack\end{matrix}$

In contrast, when the difference between φ₁ and φ₂ is mπ, m=1, 3, 5, . .. , the apparent period of the grating is 2Λ_(g) (apparent reflectivityof 1, 0, −1, 0, 1 regions assuming perfect transmission through theflexible mechanical structure 2804) and the odd diffraction orders arereflected with angles

$\begin{matrix}{{{\sin\left( \theta_{n} \right)} = {n\;\frac{\lambda}{2\Lambda_{g}}}},{n = 1},{\pm 3},{{\pm 5}\mspace{14mu}\ldots}} & \lbrack 3\rbrack\end{matrix}$

Here it is assumed that the width of the reflective fingers on thereference grating 2806A and the second grating 2806B on the flexiblemechanical structure 2804 are the same. This does not have to be thecase if the interfering beams go through different paths and experiencelosses due to reflection at various interfaces and also incidence anglevariations. The diffraction grating geometry can then be adjusted toequalize the reflected order intensities for optimized interference.

In this double grating structure, shown, for example in FIG. 28A, theintensity of the odd and even numbered orders change to 180° out ofphase with each other when the gap 2805B between the reference grating2805A and sensing grating 2806B changes. The even numbered diffractionorders are in phase with the zero order reflection considered in theprevious embodiments.

One advantage of having other off-axis even diffraction orders in phasewith the specular reflection is that it enables one to easily usedifferential techniques. This is achieved by taking the difference ofthe outputs of two detectors positioned to detect odd and even orders,respectively. Hence the common part of the laser intensity noise whichis common on both orders can be eliminated.

The sensors described herein can be used with various AFM systems andmethods to measure, for example, the attractive and repulsive forcesexperienced by the tip to provide information on various surface forcesand sample properties. Moreover, the force sensors described herein canbe used with several AFM methods, including nanoindentation, forcemodulation, ultrasonic AFM, pulsed force mode, and dynamic forcespectroscopy that have been developed to characterize the viscoelasticproperties of the material under investigation.

Thus, a force sensor for probe microscope for imaging is provided thatcan offer the unique capability for measuring interaction forces at highspeeds with high resolution. In addition to optical interferometer,various integrated readout techniques including capacitive,piezoelectric or piezoresistive can be used. Similarly, the actuatorsdescribed herein can be a thin film piezoelectric, a magnetic, or athermal actuator. Further, force sensors with multiple tips, whereseveral sensing and actuation functions are implemented in the samedevice are also envisioned. Still further, electrical measurements,chemical measurements, information storage and nanoscale manipulationscan be performed all while simultaneously obtaining topography images ofthe sample in gas or liquid media. As such, the sensors and the methodsof imaging described herein open a new area in the field of probemicroscopy. This new device can enable high speed imaging and provideimages of elastic properties and surface conditions of the sample underinvestigation.

Force sensors of the type described above in connection with the severalexemplary embodiments are particularly suitable for probe microscopedesigns and imaging methods. In the following exemplary embodiments,multi-directional manipulation of the described force sensors will beexplained for measurement of structures having three-dimensionaltopography. Movement of the force sensors is described with minimalcontact and with non-contact. In particular, the force sensors describedcan be manipulated to measure the topography of microscale and nanoscalethree dimensional structures with nanometer and sub-nanometerresolution.

The above described exemplary force sensors suitable for themulti-directional manipulation can be characterized as force sensingintegrated readout and active tip (FIRAT) type. Upon manipulating one ormore FIRAT probes in three-dimensional space with respect to an objector surface, topography of the surface or object can be obtained. Evenfurther, imaging can occur within a topographical trench or otherrecessed configuration without using an external scanner and controllerloop to scan the sample or the substrate of the FIRAT probe.

Currently, an atomic force microscope (AFM) is used as a calibrationtool for imaging critical dimensions in microelectronics due to itscapability of examining three dimensional structures. These threedimensional structures typically include those having sidewalls from 10nm to 5 μm in height. However, when measuring the sidewall structure indeep trenches, AFM cantilevers need to be tilted to have the tipinteract with the sidewall being measured. This can be inconvenient andcan prohibit imaging of both the top to bottom and sidewall profileswith acceptable throughput.

Accordingly, the exemplary embodiments that follow describe themaneuvering of the force sensor structure and more particularly theprobe tip of the force sensor structure, in different directions toprovide multiple degrees of freedom for tip motion and orientation.

Referring to FIGS. 29A and 29B, there is shown a top schematic and sidesectional schematic views of a force sensor structure 2900 in whichelectrostatic actuation is employed to enable three dimensional imagingin accordance with the present teachings.

In the exemplary embodiment, the force sensor structure 2900 cancomprise a support surface such as a substrate 2902, a flexiblemechanical structure 2904, a gap 2905, plural top electrodes such aselectrodes 2916 a-b, plural bottom electrodes such as electrodes 2920a-b, and a tip 2907. In some embodiments, the force sensor 2900 can alsoinclude a grating (not shown). According to various embodiments, theflexible mechanical structure 2904 can be fully clamped around itscircumference. Alternatively, the flexible mechanical structure 2904 canbe a clamped-clamped beam with a rectangular or H-shape, where the shortedges at the ends are clamped. Still further, the flexible mechanicalstructure 2904 can be a cantilever structure or a similar structure thatchanges shape in a predictable manner in response to a force applied tothe tip 2907. These types of structures are described above inconnection with FIGS. 10B through 10D and are applicable to the variousexemplary embodiments herein.

The tip 2907 of the force sensor structure 2900 can be made from avariety of materials that enable a high aspect ratio for the tip. Thehigh aspect ratio will ensure that deep trenches or holes of adimensional structure can be probed. For example, the tip 2907 of thesensor structure can be made from any of single crystal silicon, siliconnitride, tungsten, platinum, or other nanostructures such ascarbon-based or ZnO nanotubes. The tip 2907 can be fabricated as anintegral part of the flexible mechanical structure 2904 or can beattached to the mechanical structure 2904 using different techniquessuch as adhesives, focused ion beam deposition, or welding by help offocused ion beam deposition.

Each of the plurality of separate top electrodes 2916 a-b can beelectrically isolated and formed in the flexible mechanical structure2904. Moreover, the bottom electrodes 2920 a-b can be spaced apart fromthe separate top electrodes 2916 a-b by the gap 2905. In some cases,where the flexible mechanical structure 2904 is electrically conductive,separate bottom electrodes 2920 a-b may be required. Further, the bottomelectrodes can be positioned in the substrate 2902 and can be contactedby electrode terminals 2921 a-b, respectively. Similarly, each of theseparate top electrodes 2916 a-b can be contacted by electrode terminals2917 a-b, respectively. In some cases, the electrode terminals 2921 a-band 2917 a-b can be capacitive sensing terminals that can detect acapacitance change formed between the separate top electrodes 2916 a-band the bottom electrodes 2920 a-b.

In FIGS. 29A and 29B, a voltage can be applied between the electrodeterminals 2917 a and 2921 a as well as between electrode terminals 2917b and 2921 b. The electrode terminals therefore integrate the variouselectrodes and the voltage can be used to selectively control and moveany of the separate top electrodes 2916 a-b, so that they can serve asactuators. Further, the separate top electrodes 2916 a-b or separatebottom electrodes 2920 a-b can also perform sensing, similar to that ofa dual electrode capacitive micromachined ultrasonic transducer wherethe vibrations of the sensor flexible mechanical structure are convertedto electrical current signals through change in capacitance.

Selected ones of the electrode terminals 2917 a-b and 2921 a-b areoperable as actuators to manipulate the flexible mechanical structure2904, and thereby direct the tip 2907 of the force sensor 2900.Actuation of the actuatable electrode terminals is by known controllerswhich apply different DC bias or AC voltages of different amplitude,frequency and phase. Typically, for a clamped-clamped beam structure, atleast two of the electrostatic actuator electrodes, such aselectrostatic actuators 2917 a-b, can be selectively actuated. In thecase of a four sided beam structure, four selectively actuatedindependent actuators can be utilized as will be further described. Thismultiple electrode configuration, in addition to application of DC biasor AC voltages of different amplitude, frequency and phase enablesactuation of the fundamental and higher order symmetrical andanti-symmetrical modes of the flexible mechanical structure 2904. Thesedifferent modes can be useful for imaging the topography ofthree-dimensional structures. Furthermore, they can be useful to applyforces in three-dimensions to sample surfaces and measure theirreaction. Particular applications can include measurement of frictionforces, local piezoelectric and magnetic forces.

The force sensor 2900 can be used as described above in connection withFIG. 10A for fast imaging where bias voltages are applied between theelectrode terminals 2917 a, 2917 b and the bottom electrode terminals2920 a-b and alternating voltages of the same or reverse phase areapplied to the electrode terminals 2917 a and 2917 b to vibrate the tip2907 vertically or laterally to have intermittent contact with a samplesurface. In some cases, the forces between the tip 2907 and a close bysurface can be sensed without contact for non-contact imaging. The biasvoltages applied to the electrode terminals 2917 a, 2917 b also controlthe position of the tip 2907 in response to changes in capacitancedetected between the electrode terminals 2917 a-b and the bottomelectrode terminals 2921 a-b. An external controller (not shown) canread the detected capacitance change and generate the control signals(bias voltages) applied to the electrode terminals 2917 a-b and thebottom electrode terminals 2921 a-b.

In the exemplary embodiment, the clamped-clamped beam structure is usedto move the tip in vertical and one of the lateral directions byapplying different DC bias or AC voltages of different amplitude,frequency and phase using the two electrostatic actuator electrodes.Likewise, the structure can be extended in the other lateral directionby having a four-sided beam structure with four independent actuators.The tip 2907 of the probe can be made from a variety of materials suchas silicon, silicon nitride, tungsten, platinum or other nanostructuressuch as carbon-based or ZnO nanotubes. The important aspect of the tipstructure for topography measurement is that it has a high aspect ratioso that deep trenches or holes can be probed.

FIG. 30 shows a cross-sectional schematic diagram of generating anoscillation of the flexible mechanical structure 3004, and thereby theforce sensor tip 3007 in vertical and lateral orientations. The probetip 3007 can be vibrated in a vertical planar motion with respect to thesubstrate 3002 by exciting the first symmetric resonance of the forcesensor structure 3000. By applying a large bias voltage to control thebias position for the control loop and adding a small sinusoidal signalat the resonant frequency f₀ to the electrostatic actuation ports 3017a-b, the probe 3007 can be used for fast tapping mode or non-contactmode imaging of planar, lateral structures.

In order to impart the vertical motion, the sinusoid generated byelectrostatic actuation at 3017 a is IN PHASE with the sinusoidgenerated by the electrostatic actuation at 3017 b. With in-phasevibrations between the electrostatic actuators 3017 a-b, the flexiblemechanical structure 3004 is oscillated to an offset position 3004′. Theoffset position of the mechanical structure at 3004′ is offset from orbowed away from its original plane which is parallel to the substrate3002.

In addition to the vertical and horizontal oscillation of the mechanicalstructure 3004 of the force sensor 3000, the embodiments describedherein enable an oscillation of the probe tip 3007 an at angle normal toa three-dimensional structure as in FIG. 31A and in an elliptical orbitas shown in FIG. 31B.

A typical dimensional structure 3100 can be, for example, a portion of amicroelectronic device structure. The structure 3100 can include asubstrate or support 3102, and surface variations such as protrusions3104 and 3016 generated as a result of etching, patterning and the likeduring fabrication of a circuit or semiconductor device, for example.The surface structures 3104 and 3106 can include trenches or holes 3108between adjacent surface structures as defined by sidewalls 3110 of thesurface topography. In particular, the sidewalls 3110 can be patternedto include undercut portions 3112 as shown.

As shown in FIG. 31A, oscillating the probe tip 3107 in a desired motionpattern at an angle normal to a surface structure 3106 is suitable forinspecting a sidewall 3112 thereof. In FIG. 31B, the probe tip 3107 ismoved in an elliptical orbit to simultaneously provide both lateraltapping and vertical tapping signals. Similar motion patterns can beused for non-contact operation where the frequency shifts or oscillationamplitude variations are used to control parameters. The followingdescribes how these probe tip 3107 motion patterns can be obtained withthe force sensor of FIGS. 29A-B.

FIG. 32 is a side schematic diagram of a lateral oscillation of theforce sensor in accordance with the present teachings. It will beapparent that the force sensor shown in FIG. 32 employs the force sensorelements as described in connection with FIGS. 29A and 29B. In order toimpart motion to the probe tip 3207, different bias signals areselectively applied to the actuation ports 3217 a (also labeled as Port2) and 3217 b (also labeled as Port 1).

By applying the different bias signals to the actuation ports 3217 a and3217 b, the portions of the flexible mechanical structure 3204 close tothe fixed edges thereof can each be pulled down toward the substrate3202 by different amounts. For example, the edge of the flexiblemechanical structure 3204 closer to the actuation port 3217 b can bepulled down toward the substrate 3202 by a greater distance than theedge adjacent the actuation port 3217 a.

Since the electrodes 3216 a-b are positioned close to the edges of theflexible mechanical structure 3204, an actuation range can be the fulldistance of the gap 3205 between the flexible mechanical structure 3204and the substrate 3202. For example, with a 1-10 μm gap and a 50 μm longflexible mechanical structure 3204, the flexible mechanical structure3204 can be manipulated to form an angle in the range of 1.1° to 10°with respect to normal. Accordingly, with the probe tip 3207 seated onthe flexible mechanical structure, 3204, the probe tip will be directedat similar angles. This described range of angles is adequate fortapping on a sidewall 3110. For a 5 μm high probe tip 3207, thiscorresponds to a 100 nm to 800 nm lateral distance from the base to thetip of the probe 3207. Therefore, small objects can be imaged byselectively directing the probe tip.

In order to vibrate the tip 3207 in a linear direction at one of thedescribed angles, sinusoidal signals with proper amplitudes are added tothe actuator input signal as shown in FIG. 32. In this case a higherbias voltage is applied to the right side of the flexible mechanicalstructure 3204 as compared to the left side (V_(Dc1)>V_(DC2)). Thefrequency of this signal can be chosen to be the resonant frequency ofthe symmetric mode of the structure taking into account the effect ofthe bias voltage in the system dynamics. A similar result can beobtained using separate piezoelectric actuators (not shown) integratedto the flexible mechanical structure 3204. Similar motion can beobtained by applying AC signals higher or below the resonancefrequencies of the flexible mechanical structure 3204.

Referring now to FIG. 33, a lateral oscillation of the probe tip 3307can also be generated according to the present teachings. As with thelinear oscillation, the flexible mechanical structure 3304 ismanipulated by selective electrostatic actuation at the electrostaticactuation ports 3317 a-b. In general, the probe tip 3307 is movedlaterally using the first anti-symmetric resonance of the vibration modeof the flexible mechanical structure 3304 where the probe tip 3307 islocated at a nodal point of the structure. More specifically, thesinusoid at electrostatic actuation port 3317 b (Port 2) is excited at afirst anti-symmetric resonance of the flexible mechanical structure 3304while the sinusoid at the electrostatic actuation port 3317 a (Port 1)is excited to be OUT of phase with the sinusoid of Port 1. Thisarrangement generates a lateral movement of the probe tip 3307 withrespect to the substrate 3302.

With the probe tip 3307 at the node of this vibration mode as shown inFIG. 33, the resultant lateral motion can be used for tapping ornon-contact mode imaging of sidewalls 3110. In order to efficientlyexcite this mode, the same polarity bias (control) voltages are appliedin addition to out-of-phase sinusoidal signals at the resonantfrequency, f₁. Alternatively, in-phase sinusoidal signals at theresonant frequency f₁ can be applied in addition to bias (control)voltages of reversed polarity. Since the frequencies f₀ and f₁ can bedesigned to be far from each other and non-harmonically related, thesetwo modes can be independently excited to achieve the tip motiondepicted in FIG. 31B. In general, the voltages that can be applied tothe electrical actuation Ports 1 and 2 can be described as below.V ₁ =V _(1bias)(t)+A cos(2πf ₀ t)+B cos(2πf ₁ t) and V ₂ =V_(2bias)(t)+C cos(2πf ₀ t)+D cos)2πf ₁ t)

By way of further explanation, V_(1bias)(t) is large for controlling andbending; A cos(2πf₀ t) is for symmetric mode actuation; and B cos(2πf₁t)is for anti-symmetric mode actuation.

The relatively slowly varying V_(1bias) and V_(2bias) voltages controlthe shape of the beam, enable linearized operation of the electrostaticactuators, and are used as the actuator in the control loop. Thecoefficients A, B, C, D determine the orbit of the tip oscillation. Itis possible to have simultaneously non-zero values for all theseamplitudes to have the tip move laterally at one frequency andvertically at another. Similarly, the tip can be moved vertically usingmore than one symmetrical vibrational mode by applying appropriatesignals. By decoding and separately detecting the motions, it ispossible to run separate control loops to image lateral and verticaldimensions using model-based control and imaging software.

For fast imaging the force sensor probe tip 2907 can provide a motionrange of 2-5 μm in the vertical direction and up to 0.5 μm in the X-Ydirections by using the integrated actuators 2917 a-b. This can enablemovement of the probe tip 2907 by a range sufficient to image 100-200 nmhigh and 20 nm˜100 nm wide photoresist structures and their sidewallsencountered in microelectronics processing. The resonant frequencies canbe in the range of 1 kHz to 10 MHz depending on the speed, actuationrange, and detection limitations. Micromachined membrane, beam andcantilever based structures have been successfully developed and used inthis frequency range. The imaging described has position controlaccuracy on the order of 0.1 nm in three-dimensional space.

As indicated, the detection methods available by the present embodimentsalso include multi-directional, multi-frequency probe tip motion.

The exemplary force sensors including the tip probe 2907 enablesdetection of a force applied to the tip in different directions bymeasuring its effect on the flexible mechanical structure 2904 withmultiple detectors, and processing the detector output signals indifferent ways. These multiple detectors can use optical, capacitive,piezoresistive or piezoelectric methods.

As an example, FIG. 34A shows a side sectional schematic and FIGS. 34B,and 34C show top schematic views of a force sensor having multipleoptical detection ports in accordance with the present teachings. Inthese figures, the force sensor unit 3400 can comprise a force sensor3401, a detection surface 3402, a flexible mechanical structure 3404, agap 3405, a tip 3407, a plurality of separate top electrodes, such aselectrodes 3416 a-c, a pair of bottom electrodes, such as electrodes3420 a and 3420 b, a plurality of gratings, such as first grating 3406 aand second grating 3406 b, and at least one detector 3408. The firstgrating 3406 a can have a different grating period than the gratingperiod of 3406 b. Furthermore, the first grating 3406 a can have adifferent orientation as compared to the grating 3406 b. Thesevariations in grating structures help separate the readout beams tomeasure displacement of different parts of the flexible mechanicalstructure 3404 corresponding to different grating locations. It is to beunderstood that other force sensor embodiments described herein can alsocomprise multiple gratings and gratings fabricated at differentelevations on the detection surface 3402 to increase the deflectiondetection range.

Each of the plurality of separate top electrodes 3416 a-c can beelectrically isolated and formed in the flexible mechanical structure3404. Moreover, the bottom electrodes 3420 a-b can be spaced apart fromthe separate top electrodes 3416 a-c by the gap 3405. Further, thebottom electrodes can be positioned in the substrate 3402 and can becontacted by electrode terminals 3421 a-b. Similarly, the separate topelectrodes 3416 a and 3416 b can be contacted by electrode terminals3417 a and 3417 b.

The detection surface 3402 can be positioned at a free end of acantilever (not shown). Moreover, the flexible mechanical structure 3404can be fully clamped around its circumference, it can be aclamped-clamped beam with a rectangular or H shape where the short edgesat the ends are clamped, or it can be a cantilever structure or asimilar structure that changes shape in a predictable manner in responseto a force applied to the tip 3407.

A light beam 3410 can be directed through the detection surface 3402 toimpinge on the flexible mechanical structure 3404. The beam 3410reflects off of the flexible mechanical structure 3404, a portion ofwhich can be reflective, and is diffracted differently by the firstgrating 3406 a and the second grating 3406 b. As shown, the firstgrating 3406 a can generate a first set of diffraction orders 3412 a-band the second grating 3406 b can generate a second set of diffractionorders 3413 a-b. The detectors 3408 can detect the different diffractionorders. The detector outputs can be added to obtain up and down bendingdisplacement detection. Similarly, the outputs can be subtracted toobtain torsional motion and force detection. This information can beobtained when the spring constant for the second bending mode (torsionaround the mid axis) of the flexible mechanical structure 3404,clamped-clamped beam or a cantilever is known. Thus, in addition toacting as actuators, the first grating 3406 a and second grating 3406 bcan be used to optically or capacitively decouple the bending motionfrom the torsional motion. As such, the sensed outputs of thesedetectors yield both bending and torsional motion information.Similarly, by having a flexible mechanical structure 3404 supported by 3or 4 beams, the forces acting on the tip 3407 in three-dimensions can beobtained by proper processing of the output signals from multipledisplacement sensors, such as the gratings 3406 a, 3604 b. One can alsouse separate beams 3410 to illuminate the plurality of gratings.

More specifically, FIG. 34A further shows that the two gratings eachhave different grating periods. The first grating 3406A is positionedplaced on the left and right side of the probe tip 3407 while the secondgrating 3406 b is positioned on the right side of the probe tip 3407.When illuminated by the light beam 3410, such as a laser beam, each ofthese gratings 3406 a and 3406 b will direct the position detection (PD)signals 3412 a-b and 3413 a-b each at a different angle. By placing thephoto detectors at these particular locations the displacement of eachside of the beam can be determined. This is made clear by the top viewshown in FIG. 34B. In a similar fashion, gratings 3430 a with the sameperiodicity but different orientation from gratings 3430 b can be usedto separate the optical signals coming from each side of the probe tip3407 as shown in FIG. 34C. Since the gratings are not connected to anelectrical source, their asymmetry does not affect the electromechanicalactuation of the probe tip 3407.

Capacitive detection can be implemented into the force sensor structure3500 as shown in the exemplary embodiment of FIG. 35. The force sensorstructure 3500 includes two capacitive detection ports 3550 a and 3550 bas shown. Capacitive detection can be particularly useful when an arrayof probe tips (not shown) is formed on the same substrate for imaginglarge areas in parallel.

Similar to the force sensor structures described above, the force sensorstructure unit 3500 can comprise a force sensor 3501, a detectionsurface 3502, a flexible mechanical structure 3504, a gap 3505, a tip3507, a plurality of separate top electrodes, such as electrodes 3516a-d, and a plurality of separate bottom electrodes, such as electrodes3520 a-d.

Each of the plurality of separate top electrodes 3516 a-d can beelectrically isolated and formed in the flexible mechanical structure3504. Moreover, the bottom electrodes 3520 a-d can be spaced apart fromthe separate top electrodes 3516 a-d by the gap 3505. Further, thebottom electrodes can be positioned in the substrate 3502 and can becontacted by electrode terminals 3521 a-d. Similarly, each of theseparate top electrodes 3516 a-d can be contacted by electrode terminals3517 a-d. In the present embodiment, the electrode terminals 3517 b-ccan be capacitive sensing terminals that can detect a capacitance changeformed between the separate top electrodes 3516 b-c and the bottomelectrodes 3520 b-c.

Similar to the embodiments described above, the force sensor structure3500 of FIG. 35 includes the electrostatic actuation via electrostaticactuation ports 3517 a and 3517 d. The electrostatic actuation impartsvertical, lateral, and multidirectional motion to the probe tip 3507 asdescribed and the details are omitted herein for the sake of brevity.

FIG. 36A shows a signal processing method for obtaining lateral tappingsignals and FIG. 36B shows a signal processing method for obtainingvertical tapping signals with the exemplary force sensors in accordancewith the present teachings. More specifically, a simple differencetaking and adding scheme is utilized to generate lateral (X or Y) andvertical (Z) tapping signals during tapping mode imaging. Since thelateral motion of the tip is driven by a signal at frequency f₁, asshown in FIG. 33, and the two ends of the flexible mechanical structure3304 move out-of-phase with each other, this signal can be extracted byfiltering the input around f₁ and taking the difference of signals fromeach end. Therefore, the common mode signal indicating any motion in thevertical direction is eliminated. Similarly, the commonly known vertical(Z) tapping signal can be separated by filtering the signal aroundfrequency f₀ and summing the outputs. By designing the flexiblemechanical structure to have a large separation between f₀ and f₁, largeimaging bandwidths can be achieved around these frequencies whilesignificantly decoupling the signals. More complicated algorithms can beused to separate these signals and generate control signals to beapplied to the integrated electromechanical actuators on the sensorstructure as well as to the scanning stages.

FIG. 37 shows a signal processing for non-contact three-dimensionalimaging with exemplary force sensors in accordance with the presentteachings. For non-contact imaging, the information to run the controlloop comes from the changes in the oscillation characteristic of theforce sensor due to long range interaction forces between the tip andthe sample surface. These changes can be detected either in theoscillation amplitude or in the resonance frequency. The shifts in theseparameters can be detected by suitable circuits and can be used to runcontrol loops in the Z and X-Y directions to form three-dimensionalimages. For sensitive non-contact operation, the quality factor of theoscillator should be high. This can be ensured by designing the forcesensor structure to vibrate in a mode with low loss or operate thedevice in vacuum environment.

While the invention has been illustrated with respect to one or moreimplementations, alterations and/or modifications can be made to theillustrated examples without departing from the spirit and scope of theappended claims. In addition, while a particular feature of theinvention may have been disclosed with respect to only one of severalimplementations, such feature may be combined with one or more otherfeatures of the other implementations as may be desired and advantageousfor any given or particular function. Furthermore, to the extent thatthe terms “including”, “includes”, “having”, “has”, “with”, or variantsthereof are used in either the detailed description and the claims, suchterms are intended to be inclusive in a manner similar to the term“comprising.”

Other embodiments of the invention will be apparent to those skilled inthe art from consideration of the specification and practice of theinvention disclosed herein. It is intended that the specification andexamples be considered as exemplary only, with a true scope and spiritof the invention being indicated by the following claims.

1. A method of causing a probe tip of a force sensor structure to move in three dimensions, comprising the steps of: a. forming a flexible mechanical structure a first distance above a detection surface so as to form a gap between the flexible mechanical structure and the detection surface; b. placing the probe tip on the flexible mechanical structure so as to point toward the detection surface; c. arranging at least a pair of actuator electrodes on the flexible mechanical structure and opposed to electrodes arranged on the detection surface; d. selectively activating at least one of the actuator electrodes thereby deflecting the flexible mechanical structure at a selected location so that the flexible mechanical structure causes the probe tip to move in more than one dimension.
 2. The method according to claim 1, wherein the multi-directional motion comprises vertically oscillating the probe tip with respect to the detection surface.
 3. The method according to claim 2, wherein vertically oscillating the probe tip comprises exciting a symmetric resonance of the flexible mechanical structure.
 4. The method according to claim 1, wherein multi-directional motion comprises laterally oscillating the probe tip with respect to the detection surface.
 5. The method according to claim 4, wherein laterally oscillating the probe tip comprises applying different bias signals to the actuator electrodes such that portions of the flexible mechanical structure are deflected by correspondingly different amounts.
 6. The method according to claim 1, wherein multi-directional motion comprises oscillating the probe tip at an angle to the normal with respect to the detection surface.
 7. The method according to claim 6, wherein oscillating the tip at an angle to the normal with respect to the support surface comprises applying different bias signals to the actuator electrodes such that portions of the flexible mechanical structure are deflected by correspondingly different amounts.
 8. The method according to claim 7, wherein an angle with respect to normal is from about 0.1° to about 10°.
 9. The method according to claim 1, wherein multi-directional motion comprises an orbital motion.
 10. The method according to claim 9, wherein orbitally oscillating the tip comprises independently exciting the actuation electrodes at non-harmonic frequencies.
 11. The method according to claim 9, wherein the orbital motion is elliptical.
 12. The method according to claim 11, wherein resonant frequencies of the flexible mechanical structure are from about 1kHz to about 10MHz.
 13. The method according to claim 1, wherein the probe tip has a vertical range of motion of from about 2 μm to about 10 μm and a lateral range of up to 1 μm. 